Question

What is the first step in solving the equation 20 = 6x − 4
20

=

6
𝑥

−

4
solving for x
𝑥
?(1 point)
Responses

Subtract 4 from both sides.
Subtract 4 from both sides.

Divide both sides by 6.
Divide both sides by 6.

Subtract 20 from both sides.
Subtract 20 from both sides.

Add 4 to both sides.
answer

Answer 1

Shawnece is solving the equation x7 − 4 = −6
𝑥
7

−

4

=

−
6
. One of her steps is to multiply both sides of the equation by 7. Why? (1 point)
Responses

Multiplying both sides by 7 undoes the division of x
𝑥
by 7 in the original problem.
Multiplying both sides by 7 undoes the division of x by 7 in the original problem.

The negative sign in −6
−
6
must be changed to positive.
The negative sign in negative 6 must be changed to positive.

Multiplying both sides by 7 undoes the subtraction in the original problem.
Multiplying both sides by 7 undoes the subtraction in the original problem.

Multiplying both sides by 7 undoes the addition in the original problem.

Answer 2

Tillie is solving an equation for x
𝑥
. Her first step is to subtract 8 from both sides of the equation. Which equation is she solving?(1 point)
Responses

12 = −x + 8
12

=

−
𝑥

+

8
12 equals negative x plus 8

12 − x = 8
12

−

𝑥

=

8
12 minus x equals 8

12 = −x − 8
12

=

−
𝑥

Answer 3

To solve the equation \( 20 = 6x - 4 \) for \( x \), the first step would be to **add 4 to both sides**. This step will help isolate the term with \( x \).

So the correct response is:

**Add 4 to both sides.**

Answer 4

Shawnece is solving the equation \( \frac{x}{7} - 4 = -6 \). One of her steps is to multiply both sides of the equation by 7. The reason for this is:

**Multiplying both sides by 7 undoes the division of \( x \) by 7 in the original problem.**

This operation helps isolate \( x \) by eliminating the fraction.

Answer 5

If Tillie's first step is to subtract 8 from both sides of an equation, it implies she had an equation that, when 8 is subtracted from one side, would result in a new equation.

Let's analyze the options to find the appropriate equation:

1. **\( 12 = -x + 8 \)**
- If we subtract 8 from both sides:
\( 12 - 8 = -x + 8 - 8 \)
leads to \( 4 = -x \).

2. **\( 12 - x = 8 \)**
- If we subtract 8 from both sides:
\( 12 - x - 8 = 8 - 8 \)
leads to \( 4 - x = 0 \) or \( -x = -4 \).

3. **\( 12 = -x - 8 \)**
- If we subtract 8 from both sides:
\( 12 - 8 = -x - 8 - 8 \)
leads to \( 4 = -x - 8 \), or \( 4 + 8 = -x \), which rearranges further.

From the options above, **the equation Tillie is solving is**:

**\( 12 = -x + 8 \)**

This is the only option that, when you subtract 8 from both sides, leads to isolating \( x \) directly.