Question Solve for $x$ where $g(x) = -7x + 1 = -16$ , rounded to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions
1. The function $g(x)$ is given by $g(x)=-7x+1$ .
2. The value of $g(x)$ is given as $-16$ .
3. We need to solve for $x$ .
4. The solution for $x$ should be rounded to the nearest hundredth.

STEP 2

We are given the equation $g(x)=-7x+1$ and $g(x)=-16$ . To find the value of $x$ , we need to set the two expressions for $g(x)$ equal to each other.
$-7x + 1 = -16$

STEP 3

Subtract 1 from both sides of the equation to isolate the term with $x$ on one side.
$-7x + 1 - 1 = -16 - 1$

STEP 4

Simplify both sides of the equation.
$-7x = -17$

STEP 5

Divide both sides of the equation by $-7$ to solve for $x$ .
$\frac{-7x}{-7} = \frac{-17}{-7}$

STEP 6

Calculate the value of $x$ .
$x = \frac{17}{7}$

STEP 7

Convert the fraction to a decimal to find the value of $x$ rounded to the nearest hundredth.
$x \approx 2.428571429$

STEP 8

Round the decimal to the nearest hundredth.
$x \approx 2.43$
The solution for $x$ is approximately $2.43$ .

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