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QuestionWhich equation has a solution of t=5t=5? Choose one: a. 8t−10+2t=5t−358 t-10+2 t=5 t-35 b. 2(2t−4)−2t=−22(2 t-4)-2 t=-2 c. 3t+10=6t−53 t+10=6 t-5 d. 2−3(t+4)=2t+152-3(t+4)=2 t+15

Studdy Solution

STEP 1

Assumptions1. We have four equations to test. . We need to find which equation has a solution of t=5t=5.

STEP 2

Let's start by substituting t=5t=5 into the first equation and see if both sides are equal.
8t−10+2t=5t−358 t-10+2 t=5 t-35

STEP 3

Substitute t=5t=5 into the equation.
8(5)−10+2(5)=5(5)−358(5)-10+2(5)=5(5)-35

STEP 4

implify the equation.
40−10+10=25−3540-10+10=25-35

STEP 5

Calculate the values on both sides.
40=−1040= -10The left side does not equal the right side, so the first equation does not have a solution of t=5t=5.

STEP 6

Next, let's substitute t=5t=5 into the second equation and see if both sides are equal.
2(2t−4)−2t=−22(2 t-4)-2 t=-2

STEP 7

Substitute t=5t=5 into the equation.
2(2(5)−4)−2(5)=−22(2(5)-4)-2(5)=-2

STEP 8

implify the equation.
2(10−4)−10=−22(10-4)-10=-2

STEP 9

Calculate the values on both sides.
12=−212=-2The left side does not equal the right side, so the second equation does not have a solution of t=5t=5.

STEP 10

Next, let's substitute t=5t=5 into the third equation and see if both sides are equal.
3t+10=6t−53 t+10=6 t-5

STEP 11

Substitute t=5t=5 into the equation.
3(5)+10=6(5)−53(5)+10=6(5)-5

STEP 12

implify the equation.
15+10=30−515+10=30-5

STEP 13

Calculate the values on both sides.
25=2525=25The left side equals the right side, so the third equation has a solution of t=5t=5.

STEP 14

We have found the equation that has a solution of t=t=. Therefore, we don't need to check the fourth equation.The equation that has a solution of t=t= is3t+10=6t−3 t+10=6 t-

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