Question

The steps below show the solution to the equation 6(x - 3) = 5(x – 2). Order the reasons for the steps.

1) 6(x - 3)
2) 6(x)
3) 6(-3)
4) 6x - 18
5) 6x - 5x
6) x
7) 5(x – 2)
8) 5(x)
9) 5(–2)
10) 5x – 12
11) addition and subtraction properties of equality
12) multiply distributive property
13) add and subtract

Answer 1

The steps to solve the equation 6(x - 3) = 5(x – 2) are as follows:

Distribute the 6 on the left side: 6x - 18 = 5(x – 2)

Distribute the 5 on the right side: 6x - 18 = 5x - 10

Add 18 to both sides: 6x = 5x + 8

Subtract 5x from both sides: x = 8

Step-by-step explanation:

We can solve the equation 6(x - 3) = 5(x – 2) by distributing the terms on both sides, adding and subtracting terms on both sides, and combining like terms.

Steps 1 and 2 distribute the 6 and 5 on the left and right sides of the equation, respectively. This gives us:

6x - 18 = 5x - 10

Step 3 adds 18 to both sides of the equation. This gives us:

6x = 5x + 8

Step 4 subtracts 5x from both sides of the equation. This gives us:

x = 8

Therefore, the solution to the equation 6(x - 3) = 5(x – 2) is x = 8.