Question

5. Solve the following equations for the indicated variable.

Answer 1

Answer:a) x =−1

B) x=1/2y+12

C) m=13

D) x=2

Step-by-step explanation:a) Let's solve your equation step-by-step.

5(3x+7)=20−2(x+1)

Step 1: Simplify both sides of the equation.

5(3x+7)=20−2(x+1)

(5)(3x)+(5)(7)=20+(−2)(x)+(−2)(1)(Distribute)

15x+35=20+−2x+−2

15x+35=(−2x)+(20+−2)(Combine Like Terms)

15x+35=−2x+18

15x+35=−2x+18

Step 2: Add 2x to both sides.

15x+35+2x=−2x+18+2x

17x+35=18

Step 3: Subtract 35 from both sides.

17x+35−35=18−35

17x=−17

Step 4: Divide both sides by 17.

17x/17=−17/17

x=−1

B) Let's solve for x.

2x−y=24

Step 1: Add y to both sides.

2x−y+y=24+y

2x=y+24

Step 2: Divide both sides by 2.

2x/2=y+24/2

x=1/2y+12

C) Let's solve your equation step-by-step.

m(3−4m)=7+4(8−m2)

Step 1: Simplify both sides of the equation.

−4m2+3m=−4m2+39

Step 2: Add 4m^2 to both sides.

−4m2+3m+4m2=−4m2+39+4m2

3m=39

Step 3: Divide both sides by 3.

3m/3=39/3

m=13

D) Let's solve your equation step-by-step.

5x(x+3)=x(5x−3)+36

Step 1: Simplify both sides of the equation.

5x2+15x=5x2−3x+36

Step 2: Subtract 5x^2 from both sides.

5x2+15x−5x2=5x2−3x+36−5x2

15x=−3x+36

Step 3: Add 3x to both sides.

15x+3x=−3x+36+3x

18x=36

Step 4: Divide both sides by 18.

18x/18=36/18

x=2