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Question Find the value of xx where the linear functions g(x)=2x+11g(x) = 2x + 11 and f(x)=−2x+9f(x) = -2x + 9 intersect.

Studdy Solution

STEP 1

Assumptions
1. The function g(x) g(x) is defined as g(x)=2x+11 g(x) = 2x + 11 .
2. The function f(x) f(x) is defined as f(x)=−2x+9 f(x) = -2x + 9 .
3. We are looking for the value of x x where g(x)=f(x) g(x) = f(x) .

STEP 2

Set the two functions equal to each other to find the value of x x where g(x)=f(x) g(x) = f(x) .
g(x)=f(x) g(x) = f(x)

STEP 3

Substitute the expressions for g(x) g(x) and f(x) f(x) into the equation.
2x+11=−2x+9 2x + 11 = -2x + 9

STEP 4

Start solving for x x by moving all the x x -terms to one side of the equation. We can do this by adding 2x 2x to both sides.
2x+11+2x=−2x+9+2x 2x + 11 + 2x = -2x + 9 + 2x

STEP 5

Combine like terms on both sides of the equation.
4x+11=9 4x + 11 = 9

STEP 6

Now, isolate the x x -term by subtracting 11 11 from both sides of the equation.
4x+11−11=9−11 4x + 11 - 11 = 9 - 11

STEP 7

Simplify both sides of the equation.
4x=−2 4x = -2

STEP 8

Finally, solve for x x by dividing both sides of the equation by 4 4 .
x=−24 x = \frac{-2}{4}

STEP 9

Simplify the fraction to find the value of x x .
x=−12 x = -\frac{1}{2}
The value of x x for which g(x)=f(x) g(x) = f(x) is x=−12 x = -\frac{1}{2} .

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