Linear equation in one variable is an equation that is usually expressed in the form:<\/span><\/p>\n ay + b = 0<\/b><\/p>\n Where a<\/strong> and b<\/strong> are real numbers and y<\/strong> is a variable. This form of a linear equation has only one solution.<\/p>\n When the linear equation is plotted on a graph, the graph represents a straight line. The straight line plotted will be parallel to any of the axes. While plotting the linear equation on the x-y plane, if the variable in the equation is \u2018y\u2019, then the straight line will be parallel to the x-axis. Similarly, if the variable in the equation is \u2018x\u2019, then the straight line will be parallel to the y-axis. The solution of the equation will be the point where the straight line intersects any of the two axes.<\/p>\n <\/p>\n For example, 14y + 8 = 20<\/strong> is a linear equation having a single variable \u2018y\u2019 in it.<\/p>\n Here the variable is \u2018y\u2019 hence, the straight line is parallel to the x-axis. The solution of this line is the point where the straight line intersects the y-axis.<\/p>\n <\/p>\n <\/b><\/p>\n A linear equation is a type of equation in which the degree of each variable in the equation is equal to one.<\/p>\n For example, 3x + 20 = 5<\/strong> is a linear equation as the degree of \u2018x<\/strong>\u2019 is 1. Whereas, an equation, x^{2}+16=20 <\/span> is not a linear equation as the degree of \u2018<\/span>x<\/b>\u2019 is <\/span>2<\/b> in this case.\u00a0<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n The general form is <\/span>ax + c = 0<\/b>. Here a <\/strong><\/span>is the coefficient of x.\u00a0 <\/span>x<\/b> is the variable. <\/span>c<\/b> is the constant term. The coefficient and the constant term should be separated to find the final solution of this linear equation.<\/span><\/p>\n \u00a0<\/span><\/span><\/p>\n <\/b><\/p>\n <\/span><\/p>\n For the general form, i.e., <\/span>ax + c = 0<\/b>,<\/span><\/p>\n First, the constant term \u2018c\u2019 is moved to the right side,<\/span><\/p>\n \\Rightarrow a x=-c<\/span><\/span><\/p>\n Now to find the value of x we divide the above equation on both sides by \u2018a\u2019,<\/span><\/p>\n \\Rightarrow \\mathrm{x}=-\\frac{c}{a}<\/span><\/span><\/p>\n which is the solution of the equation.<\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n Example 1<\/b>: Consider the equation: 14x \u2013 18 = 8x + 42<\/strong><\/span><\/p>\n <\/strong><\/span><\/p>\n Step 1<\/b>: Isolate all the variables on one side of the equation i.e., shift the variables from one side of the equation to the other side of the equation.<\/span><\/p>\n In the equation 14x \u2013 18 = 8x + 42<\/strong>, we transpose 8x from the right-hand side to the left-hand side of the equality, the operation gets reversed upon transposition and the equation becomes:<\/span><\/span><\/span><\/p>\n \u00a014x \u2013 18 \u2013 8x = 42<\/span><\/span><\/p>\n \\Rightarrow 6 x-18=42<\/span><\/span><\/p>\n <\/span><\/p>\n Step 2<\/b>: Similarly shifting the constant terms to the other side of the equation:<\/span><\/span><\/p>\n \u00a0 \u00a06x \u2013 18 = 42<\/span><\/span><\/span><\/p>\n \u00a0<\/span>\u21d2<\/span> 6x = 42 + 18<\/span><\/span><\/p>\n \u00a0<\/span>\u21d2<\/span> 6x = 60<\/span><\/p>\n <\/span><\/p>\n Step 3<\/b>: Divide the equation with 6 on both sides of the equality.<\/span><\/span><\/p>\n <\/span><\/p>\n \\Rightarrow \\frac{6x}{6}=\\frac{60}{6}<\/span><\/strong><\/p>\n \\Rightarrow x=10<\/span><\/strong><\/p>\n If we substitute x = 10 in the equation 14x \u201318 = 8x + 42<\/strong>, we will get 122 = 122\u00a0<\/strong> which satisfies the equality and hence is the required solution.<\/span><\/p>\n <\/p>\n Example 2<\/b>: Fifteen years ago, Arjun was one-fourth of what his age is now. How old is Arjun?<\/span><\/p>\n <\/span><\/p>\n Solution<\/b>:<\/span><\/p>\n Let Arjun’s present age be x years.<\/span><\/span><\/p>\n Hence, fifteen years ago, Arjun’s age was (x-15) years. According to the given information,<\/span><\/p>\n x – 15 = x\/4 \u21d2 4(x – 15) = 4x\/4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[Multiplying 4 on both sides of the equation]<\/span><\/span><\/span><\/p>\n \u21d2 4x – 60 = x\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0[Simplifying the equation]<\/span><\/span><\/p>\n \u21d2 4x – x = 60<\/span><\/span><\/p>\n \u21d2 3x = 60<\/span><\/span><\/p>\n \u21d2 x = 60\/3<\/span><\/span><\/p>\n Hence, x = 20.<\/span><\/p>\n Therefore, Arjun is 20 years old.<\/strong><\/p>\n <\/strong><\/p>\n <\/strong><\/p>\n Example 3<\/b>: Find two numbers such that one of the numbers is 6 more than the other and the sum of the two numbers is 28.<\/span><\/p>\n <\/span><\/p>\n Solution<\/b>:\u00a0<\/span><\/p>\n We do not know either of the two numbers, and we need to find them.<\/span><\/p>\n Two conditions are given:<\/span><\/span><\/p>\n Let the smaller number be x, then the larger number is 6 more than x, i.e., x\u00a0 + 6.<\/span><\/p>\n The other condition says that the sum of these two numbers x and x\u00a0 + 6 is 28.<\/span><\/p>\n This means that\u00a0 x\u00a0 + (x\u00a0 + 6) = 28<\/span><\/span><\/p>\n 2 x+6=28 \\Rightarrow 2 x=28-6 = 22<\/span><\/span><\/span><\/p>\n \\therefore x=\\frac{22}{2}=11<\/span><\/span><\/span><\/p>\n Now, x + 6 = 11 + 6 = 17<\/span><\/p>\n Therefore, the two numbers which have a difference of 6 and their sum is 28 are <\/span>11<\/b> and <\/span>17<\/b>.\u00a0<\/span><\/p>\n <\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/leio-300x157.png\")
<\/h2>\nWhat is a linear equation?<\/b><\/h2>\n
Standard Form<\/b>\u00a0<\/b><\/h2>\n
Solving linear equation in one variable involves the following steps:<\/b><\/h2>\n
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Examples<\/b><\/h2>\n
<\/span><\/span><\/p>\n\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n