[latex]frac{1}{8}x+frac{1}{2}=frac{1}{4}quad{LCD=8}[/latex] | |
Multiply both sides of the equation by that LCD, [latex]8[/latex]. This clears the fractions. | [latex]color{red}{8(}frac{1}{8}x+frac{1}{2}color{red}{)}=color{red}{8(}frac{1}{4}color{red}{)}[/latex] |
Use the Distributive Property. | [latex]8cdotfrac{1}{8}x+8cdotfrac{1}{2}=8cdotfrac{1}{4}[/latex] |
Simplify — and notice, no more fractions! | [latex]x+4=2[/latex] |
Solve using the General Strategy for Solving Linear Equations. | [latex]x+4color{red}{-4}=2color{red}{-4}[/latex] |
Simplify. | [latex]x=-2[/latex] |
Check: Let [latex]x=-2[/latex] [latex]frac{1}{8}x+frac{1}{2}=frac{1}{4}[/latex] [latex]frac{1}{8}(color{red}{-2})+frac{1}{2}stackrel{text{?}}{=}frac{1}{4}[/latex] [latex]frac{-2}{8}+frac{1}{2}stackrel{text{?}}{=}frac{1}{4}[/latex] [latex]frac{-2}{8}+frac{4}{8}stackrel{text{?}}{=}frac{1}{4}[/latex] Path finder 8 2 4 download free. [latex]frac{2}{8}stackrel{text{?}}{=}frac{1}{4}[/latex] [latex]frac{1}{4}=frac{1}{4}quadcheckmark[/latex] |
Find the least common denominator of all the fractions in the equation. | [latex]7=frac{1}{2}x+frac{3}{4}x-frac{2}{3}xquad{LCD=12}[/latex] |
Multiply both sides of the equation by [latex]12[/latex]. | [latex]color{red}{12}(7)=color{red}{12}cdot(frac{1}{2}x+frac{3}{4}x-frac{2}{3}x)[/latex] |
Distribute. | [latex]12(7)=12cdotfrac{1}{2}x+12cdotfrac{3}{4}x-12cdotfrac{2}{3}x[/latex] |
Simplify — and notice, no more fractions! | [latex]84=6x+9x-8x[/latex] |
Combine like terms. | [latex]84=7x[/latex] |
Divide by [latex]7[/latex]. | [latex]frac{84}{color{red}{7}}=frac{7x}{color{red}{7}}[/latex] |
Simplify. | [latex]12=x[/latex] |
Check: Let [latex]x=12[/latex]. | |
[latex]7=frac{1}{2}x+frac{3}{4}x-frac{2}{3}x[/latex] [latex]7stackrel{text{?}}{=}frac{1}{2}(color{red}{12})+frac{3}{4}(color{red}{12})-frac{2}{3}(color{red}{12})[/latex] [latex]7stackrel{text{?}}{=}6+9-8[/latex] [latex]7=7quadcheckmark[/latex] |
Find the LCD of all the fractions in the equation. | [latex]x+frac{1}{3}=frac{1}{6}x-frac{1}{2},quad{LCD=6}[/latex] |
Multiply both sides by the LCD. | [latex]color{red}{6}(x+frac{1}{3})=color{red}{6}(frac{1}{6}x-frac{1}{2})[/latex] |
Distribute. | [latex]6cdot{x}+6cdotfrac{1}{3}=6cdotfrac{1}{6}x-6cdotfrac{1}{2}[/latex] |
Simplify — no more fractions! | [latex]6x+2=x-3[/latex] |
Subtract [latex]x[/latex] from both sides. | [latex]6x-color{red}{x}+2=x-color{red}{x}-3[/latex] |
Simplify. | [latex]5x+2=-3[/latex] |
Subtract 2 from both sides. | [latex]5x+2color{red}{-2}=-3color{red}{-2}[/latex] |
Simplify. | [latex]5x=-5[/latex] |
Divide by [latex]5[/latex]. | [latex]frac{5x}{color{red}{5}}=frac{-5}{color{red}{5}}[/latex] |
Simplify. | [latex]x=-1[/latex] |
Check: Substitute [latex]x=-1[/latex]. | |
[latex]x+frac{1}{3}=frac{1}{6}x-frac{1}{2}[/latex] [latex](color{red}{-1})+frac{1}{3}stackrel{text{?}}{=}frac{1}{6}(color{red}{-1})-frac{1}{2}[/latex] [latex](-1)+frac{1}{3}stackrel{text{?}}{=}-frac{1}{6}-frac{1}{2}[/latex] [latex]-frac{3}{3}+frac{1}{3}stackrel{text{?}}{=}-frac{1}{6}-frac{3}{6}[/latex] [latex]-frac{2}{3}stackrel{text{?}}{=}-frac{4}{6}[/latex] [latex]-frac{2}{3}=-frac{2}{3}quadcheckmark[/latex] |
[latex]1=frac{1}{2}(4x+2)[/latex] | |
Distribute. | [latex]1=frac{1}{2}cdot4x+frac{1}{2}cdot2[/latex] |
Simplify. Now there are no fractions to clear! | [latex]1=2x+1[/latex] |
Subtract 1 from both sides. | [latex]1color{red}{-1}=2x+1color{red}{-1}[/latex] |
Simplify. | [latex]0=2x[/latex] |
Divide by [latex]2[/latex]. | [latex]frac{0}{color{red}{2}}=frac{2x}{color{red}{2}}[/latex] |
Simplify. | [latex]0=x[/latex] |
Check: Let [latex]x=0[/latex]. | |
[latex]1=frac{1}{2}(4x+2)[/latex] [latex]1stackrel{text{?}}{=}frac{1}{2}(4(color{red}{0})+2)[/latex] [latex]1stackrel{text{?}}{=}frac{1}{2}(2)[/latex] [latex]1stackrel{text{?}}{=}frac{2}{2}[/latex] [latex]1=1quadcheckmark[/latex] |