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The equation of a function is [tex]y = 4x - 1 \frac{1}{2}[/tex]. Find the value of [tex]y[/tex] when:

(a) [tex]x = 12[/tex]

(b) [tex]x = 2 \frac{1}{2}[/tex]

(c) [tex]x = -\frac{1}{2}[/tex]

Sagot :

GinnyAnsweridn
Let's solve the problem step-by-step.

Given the equation of the function:
[tex]\[ y = 4x - 1.5 \][/tex]

We need to find the values of [tex]\( y \)[/tex] for different given values of [tex]\( x \)[/tex].

### Part (a): When [tex]\( x = 12 \)[/tex]

Substitute [tex]\( x = 12 \)[/tex] into the equation:
[tex]\[ y = 4(12) - 1.5 \][/tex]
[tex]\[ y = 48 - 1.5 \][/tex]
[tex]\[ y = 46.5 \][/tex]

So, when [tex]\( x = 12 \)[/tex], [tex]\( y = 46.5 \)[/tex].

### Part (b): When [tex]\( x = 2.5 \)[/tex] (Note that [tex]\( 2 \frac{1}{2} = 2.5 \)[/tex])

Substitute [tex]\( x = 2.5 \)[/tex] into the equation:
[tex]\[ y = 4(2.5) - 1.5 \][/tex]
[tex]\[ y = 10 - 1.5 \][/tex]
[tex]\[ y = 8.5 \][/tex]

So, when [tex]\( x = 2.5 \)[/tex], [tex]\( y = 8.5 \)[/tex].

### Part (c): When [tex]\( x = -0.5 \)[/tex] (Note that [tex]\( -\frac{1}{2} = -0.5 \)[/tex])

Substitute [tex]\( x = -0.5 \)[/tex] into the equation:
[tex]\[ y = 4(-0.5) - 1.5 \][/tex]
[tex]\[ y = -2 - 1.5 \][/tex]
[tex]\[ y = -3.5 \][/tex]

So, when [tex]\( x = -0.5 \)[/tex], [tex]\( y = -3.5 \)[/tex].

### Summary

(a) When [tex]\( x = 12 \)[/tex], [tex]\( y = 46.5 \)[/tex].

(b) When [tex]\( x = 2.5 \)[/tex], [tex]\( y = 8.5 \)[/tex].

(c) When [tex]\( x = -0.5 \)[/tex], [tex]\( y = -3.5 \)[/tex].
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