If f(x) = -5(2x + 1) and f(x) = -35, find x.

Answer 1

The equations are given as:

f(x) = -5(2x + 1) and f(x) = -35

Since both equations equal f(x), they can be set as equal to each other to find x.

-5(2x+1) = -35

Distribute on the first side of the equation.

-10x - 5 = -35

+5 +5

-10x = -30

Divide both sides of the equation by -10 to solve for x.

-10x = -30

-10 -10

x= 3

Check your answer by putting the value of x into the original equation containing x.

f(3) = -5[(2 x 3) + 1] = -5(6 +1) = -35

Since f(x) is also given as -35 it confirms that x = 3

Answer 2

f(x) is a term that feels really abstract when you're first learning math. To simplify this, replace it with a measurement type that makes more sense to you. In this case, I will use change in speed.

If f(x) = -5(2x + 1) and f(x) = -35 then we can also say:

speed change = -5(2x + 1) and speed change = -35

Since both of these values are meant to be the same change in speed we can solve for x by setting them equal to each other.

-5(2x + 1) = -35

Now we can multiply the -5 through on the left side. Remember when parentheses are used the multiplier must be distributed to both terms. -5 * 2x = -10x and -5 * 1 = -5 so:

-10x - 5 = -35

Then we add the 5 to both sides to get the x term by itself.

-10x = -30

And finally we divide by -10 to get our solution for x. Remember that dividing by a negative changes the sign on the other side of the equation, in this case from a (-) to a (+). Therefore,

x = 3