Certainly! Let's solve this step-by-step.
We are given that [tex]\( x = 4 \)[/tex] and we need to frame three equations with [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
### Equation 1
First equation: [tex]\( y = 2x + 3 \)[/tex]
1. Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[
y = 2(4) + 3
\][/tex]
2. Simplify the multiplication:
[tex]\[
y = 8 + 3
\][/tex]
3. Perform the addition:
[tex]\[
y = 11
\][/tex]
So, for the first equation [tex]\( y = 11 \)[/tex].
### Equation 2
Second equation: [tex]\( y = x^2 - 5x + 6 \)[/tex]
1. Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[
y = 4^2 - 5(4) + 6
\][/tex]
2. Simplify the exponentiation and multiplication:
[tex]\[
y = 16 - 20 + 6
\][/tex]
3. Perform the arithmetic operations:
[tex]\[
y = 16 - 20 + 6 = -4 + 6 = 2
\][/tex]
So, for the second equation [tex]\( y = 2 \)[/tex].
### Equation 3
Third equation: [tex]\( y = \frac{x}{2} + 7 \)[/tex]
1. Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[
y = \frac{4}{2} + 7
\][/tex]
2. Simplify the division:
[tex]\[
y = 2 + 7
\][/tex]
3. Perform the addition:
[tex]\[
y = 9
\][/tex]
So, for the third equation [tex]\( y = 9 \)[/tex].
### Summary
The results from framing and solving the given equations with [tex]\( x = 4 \)[/tex] are:
- For the equation [tex]\( y = 2x + 3 \)[/tex], [tex]\( y = 11 \)[/tex].
- For the equation [tex]\( y = x^2 - 5x + 6 \)[/tex], [tex]\( y = 2 \)[/tex].
- For the equation [tex]\( y = \frac{x}{2} + 7 \)[/tex], [tex]\( y = 9 \)[/tex].
Therefore, the calculated values are:
[tex]\[
(11, 2, 9)
\][/tex]
