LaTeX: \Delta QRS\cong\Delta TUV,\:QS=3v+2,Δ Q R S ≅ Δ T U V , Q S = 3 v + 2 , and LaTeX: TV=7v-6,T V = 7 v − 6 , enter the lengths of QS

The length of QS = 8

Step-by-step explanation:

From the above question:

Δ Q R S ≅ Δ T U V

Q S = 3 v + 2 , and T V = 7 v − 6 , enter the lengths of QS

Hence:

Step 1

We solve for v

QS = TV

3v + 2 = 7v - 6

Collect like ters

2 + 6 = 7v - 3v

8 = 4v

v = 8/4

v = 2

Step 2

Solving for Q S

Q S = 3 v + 2

v = 2

QS = 3(2) + 2

QS = 6 + 2

QS = 8

The length of QS = 8

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

replication and blocking

step-by-step explanation: