4(t-1)8=2(t+3)8

Reduce the expression 4(t-1)8 by cancelling the common factors.

Factor 4 out of 8.

4(t-1)4⋅2=2(t+3)8

Cancel the common factor.

4(t-1)4⋅2=2(t+3)8

Rewrite the expression.

t-12=2(t+3)8

t-12=2(t+3)8

Reduce the expression 2(t+3)8 by cancelling the common factors.

Factor 2 out of 8.

t-12=2(t+3)2⋅4

Cancel the common factor.

t-12=2(t+3)2⋅4

Rewrite the expression.

t-12=t+34

t-12=t+34

t-12=t+34

Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 4. The t-12 expression needs to be multiplied by 22 to make the denominator 4.

t-12⋅22=t+34

Multiply the expression by a factor of 1 to create the least common denominator (LCD) of 4.

(t-1)(2)

Simplify.

Apply the distributive property.

t⋅2-1⋅24=t+34

Simplify the expression.

Move 2 to the left of t.

2⋅t-1⋅24=t+34

Multiply -1 by 2.

2t-24=t+34

2t-24=t+34

2t-24=t+34

2t-24=t+34

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

2t-2=t+3

Subtract t from both sides of the equation.

2t-2-t=3

Subtract t from 2t.

t-2=3

t-2=3

Add 2 to both sides of the equation.

t=3+2

Add 3 and 2.

t=5

t=5

Solve for t (4(t-1))/8=(2(t+3))/8