https://file.aiquickdraw.com/mathbot/file/17280113226929e8lpk5z.jpg

We are given the function \( j(x) = -\frac{4}{5}x + 7 \) and need to find the value of \( x \) such that \( j(x) = -5 \).

To solve this, we substitute \( j(x) = -5 \) into the equation:

\[
-5 = -\frac{4}{5}x + 7
\]

### Step 1: Isolate the term with \( x \)
Subtract 7 from both sides:

\[
-5 - 7 = -\frac{4}{5}x
\]

\[
-12 = -\frac{4}{5}x
\]

### Step 2: Solve for \( x \)
Multiply both sides of the equation by the reciprocal of \( -\frac{4}{5} \), which is \( -\frac{5}{4} \):

\[
x = -12 \times -\frac{5}{4}
\]

\[
x = 60/4
\]

\[
x = 15
\]

So, the value of \( x \) is \( \boxed{15} \).

Let me know if you would like more details or have any questions. 

Here are some related questions:
1. What happens to the function if \( j(x) = 0 \)?
2. How would the solution change if the slope was positive instead of negative?
3. Can you graph this function and identify where \( j(x) = -5 \)?
4. What is the y-intercept of this linear function?
5. How do we interpret the slope \( -\frac{4}{5} \) in this context?

**Tip:** When dealing with fractional coefficients, multiplying by the reciprocal is a key step to eliminate the fraction and isolate the variable.

Find the value of x so that the function has the given value: j(x) = -4/5x + 7; j(x) = -5.

Learn how to find the value of x for the linear equation j(x) = -4/5x + 7 when j(x) equals -5. Follow a step-by-step breakdown of isolating the variable x, solving linear equations, and understanding fractional coefficients. Ideal for Grades 8-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation