What value or values of x satisfy 2|x + 5.3| = 4.2? x can only equal –3.2. x can only equal 7.4. x can equal –3.2 or –7.4. x can equal –3.2 or 7.4.

Step-by-step explanation:

We need to know how to deal with absolute values to solve this. Remember that absolute value is a distance measure, not a counting number. The absolute value is the distance that 2 numbers are away from a specific number on the number line; the distance from the number will be the same distance going right and left of the number. For example, if we are looking for the numbers that are 3 units from 0 on a number line, the 2 numbers that are 3 units away are 3 and -3.

We will simplify our absolute value equation a bit first by dividing away the 2 out front. It is very important that you realize/remember that you cannot distribute into absolute value signs the way you would parenthesis!! Dividing away the 2 gives us

| x + 5.3 | = 2.1

In words, this problem is asking us for the 2 values that are 2.1 units from 5.3 on a number line. Hence, when we remove the absolute value signs, we set the equation equal to both 2.1 and -2.1 because we want the values 2.1 units to the right AND left of 5.3:

x + 5.3 = 2.1   or   x + 5.3 = -2.1 and we solve both:

for the first one, x = -3.2 and for the second one, x = -7.4.  Your option is the third one: "x can equal -3.2 or -7.4".

answer: true

step-by-step explanation: