Let's solve the given equation step-by-step:
[tex]\[ 2 = -\frac{7}{4} + \frac{1}{4} x \][/tex]
### Step 1:
First, add [tex]\(\frac{7}{4}\)[/tex] to both sides of the equation to isolate the term with [tex]\(x\)[/tex].
[tex]\[ 2 + \frac{7}{4} = -\frac{7}{4} + \frac{7}{4} + \frac{1}{4} x \][/tex]
Adding [tex]\(\frac{7}{4}\)[/tex] to [tex]\(-\frac{7}{4}\)[/tex] cancels out on the right side, simplifying the equation:
[tex]\[ 2 + \frac{7}{4} = \frac{1}{4} x \][/tex]
Now, combine the fractions on the left-hand side:
[tex]\[ 2 = \frac{8}{4} \][/tex]
[tex]\[ 2 + \frac{7}{4} = \frac{8}{4} + \frac{7}{4} = \frac{15}{4} \][/tex]
So, we have:
[tex]\[ \frac{15}{4} = \frac{1}{4} x \][/tex]
### Step 2:
Next, multiply both sides by 4 to solve for [tex]\(x\)[/tex].
[tex]\[ 4 \times \frac{15}{4} = 4 \times \frac{1}{4} x \][/tex]
The 4s cancel out on the right side:
[tex]\[ 15 = x \][/tex]
So, the solution to the equation is:
[tex]\[ x = 15 \][/tex]
### Filling in the blanks:
1. Add [tex]\(\frac{7}{4}\)[/tex] to both sides.
2. Multiply both sides by 4.
The solution is:
[tex]\[ x = 15 \][/tex] ✔
Checking the solution, we successfully solved the two-step equation and isolated [tex]\(x\)[/tex].
