Solve 7(v-1)=7v+4-4(-3v-1)

$$7 ( v - 1 ) = 7 v + 4 - 4 ( - 3 v - 1 )$$

Solve for v

$$v = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by v-1.

$$7v-7=7v+4-4\left(-3v-1\right)$$

Use the distributive property to multiply -4 by -3v-1.

$$7v-7=7v+4+12v+4$$

Combine 7v and 12v to get 19v.

$$7v-7=19v+4+4$$

Add 4 and 4 to get 8.

$$7v-7=19v+8$$

Subtract 19v from both sides.

$$7v-7-19v=8$$

Combine 7v and -19v to get -12v.

$$-12v-7=8$$

Add 7 to both sides.

$$-12v=8+7$$

Add 8 and 7 to get 15.

$$-12v=15$$

Divide both sides by -12.

$$v=\frac{15}{-12}$$

Reduce the fraction \frac{15}{-12} to lowest terms by extracting and canceling out 3.

$$v=-\frac{5}{4}$$