Certainly! Let's solve for [tex]\( x \)[/tex] in each of the given equations step-by-step:
### Part (a):
The equation given is:
[tex]\[ \frac{5x}{2} + 1 = 11 \][/tex]
Step 1: Subtract 1 from both sides of the equation to isolate the term involving [tex]\( x \)[/tex].
[tex]\[ \frac{5x}{2} + 1 - 1 = 11 - 1 \][/tex]
[tex]\[ \frac{5x}{2} = 10 \][/tex]
Step 2: Multiply both sides of the equation by 2 to eliminate the fraction.
[tex]\[ 2 \cdot \frac{5x}{2} = 2 \cdot 10 \][/tex]
[tex]\[ 5x = 20 \][/tex]
Step 3: Divide both sides of the equation by 5 to solve for [tex]\( x \)[/tex].
[tex]\[ x = \frac{20}{5} \][/tex]
[tex]\[ x = 4 \][/tex]
So, the value of [tex]\( x \)[/tex] in part (a) is [tex]\( x = 4 \)[/tex].
### Part (b):
The equation given is:
[tex]\[ \frac{2x}{7} - 3 = 2 \][/tex]
Step 1: Add 3 to both sides of the equation to isolate the term involving [tex]\( x \)[/tex].
[tex]\[ \frac{2x}{7} - 3 + 3 = 2 + 3 \][/tex]
[tex]\[ \frac{2x}{7} = 5 \][/tex]
Step 2: Multiply both sides of the equation by 7 to eliminate the fraction.
[tex]\[ 7 \cdot \frac{2x}{7} = 7 \cdot 5 \][/tex]
[tex]\[ 2x = 35 \][/tex]
Step 3: Divide both sides of the equation by 2 to solve for [tex]\( x \)[/tex].
[tex]\[ x = \frac{35}{2} \][/tex]
[tex]\[ x = 17.5 \][/tex]
So, the value of [tex]\( x \)[/tex] in part (b) is [tex]\( x = 17.5 \)[/tex].
### Summary:
- In equation (a), [tex]\( x = 4 \)[/tex].
- In equation (b), [tex]\( x = 17.5 \)[/tex].
