Solve the following equation: 2x – 31 = 3(x + 2) (1 point)

Question

37
–37
5
37/5

Answer 1

To solve for x, we can first distribute the 3 to both terms inside the parentheses:

2x - 31 = 3x + 6

Next, we can move the 3x term to the left side of the equation by subtracting 3x from both sides:

2x - 3x - 31 = 3x - 3x + 6

Simplifying further, we have:

-x - 31 = 6

To isolate x, we can add 31 to both sides:

-x - 31 + 31 = 6 + 31

-x = 37

Finally, we can multiply both sides by -1 to solve for x:

(-1)(-x) = (-1)(37)

x = -37

So, the solution to the equation is x = -37.

Answer 2

Find the range of the function f(x) = 4x – 1 for the domain {–1, 0, 1, 2, 3}.
(1 point)
{–5, –3, 0, 7, 11} {–5, –4, –3, –2, –1} {–11, –7, –3, 1, 5} {–5, –1, 3, 7, 11}

Answer 3

To find the range of the function f(x) = 4x - 1 for the given domain {-1, 0, 1, 2, 3}, we need to substitute each value from the domain into the function and find the corresponding output.

When x = -1:
f(-1) = 4(-1) - 1 = -5

When x = 0:
f(0) = 4(0) - 1 = -1

When x = 1:
f(1) = 4(1) - 1 = 3

When x = 2:
f(2) = 4(2) - 1 = 7

When x = 3:
f(3) = 4(3) - 1 = 11

The outputs for each value in the domain are {-5, -1, 3, 7, 11}.

Therefore, the range of the function is {–5, –1, 3, 7, 11}.

Answer 4

Find the slope of the graph of the following: 9x – 3y = 15 (1 point)
–3
3
-1/3
1/3

Answer 5

To find the slope of the graph of the equation 9x - 3y = 15, we need to rewrite the equation in slope-intercept form, which is in the form y = mx + b, where m represents the slope.

Let's start by moving the 9x term to the right side of the equation:

-3y = -9x + 15

Next, we can divide both sides of the equation by -3 to solve for y:

(-3y)/-3 = (-9x + 15)/-3

Simplifying further, we have:

y = 3x - 5

Comparing the equation to y = mx + b, we can see that the slope, m, is 3.

Therefore, the slope of the graph of the equation 9x - 3y = 15 is 3.

Answer 6

What is the slope-intercept form of the equation 4x + 2y = 6? (1 point)
y = 2x + 3 y = 2x – 3 y = –2x – 3 y = –2x + 3

Answer 7

To find the slope-intercept form of the equation 4x + 2y = 6, we need to solve for y.

First, let's isolate the term with y by moving the 4x term to the right side of the equation:

2y = -4x + 6

Next, divide both sides of the equation by 2 to solve for y:

(2y)/2 = (-4x + 6)/2

Simplifying further, we have:

y = -2x + 3

Therefore, the slope-intercept form of the equation 4x + 2y = 6 is y = -2x + 3.