Summarize:

5(x+4)=6x5{\displaystyle 5(x+4)=6x-5}. Use the distributive property to cancel the parentheses:5(x+4)=6x5{\displaystyle 5(x+4)=6x-5}5x+20=6x5{\displaystyle 5x+20=6x-5} Cancel the 5x{\displaystyle 5x} on the left side of the equation by subtracting 5x{\displaystyle 5x} from both sides:5x+20=6x5{\displaystyle 5x+20=6x-5}5x+205x=6x55x{\displaystyle 5x+20-5x=6x-5-5x}20=x5{\displaystyle 20=x-5} Isolate the variable by adding 5 to each side of the equation:20=x5{\displaystyle 20=x-5}20+5=x5+5{\displaystyle 20+5=x-5+5}25=x{\displaystyle 25=x} 7+3x=7x2{\displaystyle -7+3x={
rac {7-x}{2}}}. Remove the fraction. To do this, multiply each side of the equation by the fraction's denominator:7+3x=7x2{\displaystyle -7+3x={
rac {7-x}{2}}}2(7+3x)=2(7x2){\displaystyle 2(-7+3x)=2({
rac {7-x}{2}})}14+6x=7x{\displaystyle -14+6x=7-x} Cancel the x{\displaystyle -x} on the right side of the equation by adding x{\displaystyle x} to each side of the equation:14+6x=7x{\displaystyle -14+6x=7-x}14+6x+x=7x+x{\displaystyle -14+6x+x=7-x+x}14+7x=7{\displaystyle -14+7x=7} Move the constants to one side of the equation by adding 14 to each side:14+7x=7{\displaystyle -14+7x=7}14+7x+14=7+14{\displaystyle -14+7x+14=7+14}7x=21{\displaystyle 7x=21} Cancel the coefficient by dividing each side of the equation by 7:7x=21{\displaystyle 7x=21}7x7=217{\displaystyle {
rac {7x}{7}}={
rac {21}{7}}}x=3{\displaystyle x=3} 9x+15=12y;9y=9x+27{\displaystyle 9x+15=12y;9y=9x+27} Isolate the y{\displaystyle y} variable in the second equation:9y=9x+27{\displaystyle 9y=9x+27}9y=9(x+3){\displaystyle 9y=9(x+3)}9y9=9(x+3)9{\displaystyle {
rac {9y}{9}}={
rac {9(x+3)}{9}}}y=x+3{\displaystyle y=x+3} Plug in x+3{\displaystyle x+3} for y{\displaystyle y} in the first equation:9x+15=12y{\displaystyle 9x+15=12y}9x+15=12(x+3){\displaystyle 9x+15=12(x+3)} Use the distributive property to cancel the parentheses:9x+15=12x+36{\displaystyle 9x+15=12x+36} Cancel the variable on the left side of the equation by subtracting 9x{\displaystyle 9x} from each side:9x+15=12x+36{\displaystyle 9x+15=12x+36}9x+159x=12x+369x{\displaystyle 9x+15-9x=12x+36-9x}15=3x+36{\displaystyle 15=3x+36} Move the constants to one side by subtracting 36 from each side:15=3x+36{\displaystyle 15=3x+36}1536=3x+3636{\displaystyle 15-36=3x+36-36}21=3x{\displaystyle -21=3x} Cancel the coefficient by dividing each side by 3:21=3x{\displaystyle -21=3x}213=3x3{\displaystyle {
rac {-21}{3}}={
rac {3x}{3}}}7=x{\displaystyle -7=x} Solve for y{\displaystyle y} by plugging the value of x{\displaystyle x} into either equation:9y=9x+27{\displaystyle 9y=9x+27}9y=9(7)+27{\displaystyle 9y=9(-7)+27}9y=63+27{\displaystyle 9y=-63+27}9y=36{\displaystyle 9y=-36}9y9=369{\displaystyle {
rac {9y}{9}}={
rac {-36}{9}}}y=4{\displaystyle y=-4}
Try this problem using the distributive property with one variable: Try this problem involving a fraction: Try solving this system of equations: