Substitute each value for x into the absolute value equation to solve this problem. Start with A. x = 4/5.
|(4/5) + 3| = 4(4/5) - 7
Add 4/5 and 3 inside the absolute value symbols, and multiply 4 times 4/5 on the right side of the equation.
|19/5| = 16/5 - 7
Subtract 16/5 and 7.
|19/5| = -19/5, which is a false statement because the absolute value of 19/5 is 19/5, and 19/5 does not equal -19/5. This cancels out A from our possible solutions.
Now substitute B. x = 10/3 into the equation.
|(10/3) + 3| = 4(10/3) - 7
Add 10/3 and 3 inside the absolute values, and multiply 4 times 10/3 on the right side of the equation.
|19/3| = 40/3 - 7
Subtract 40/3 and 7.
|19/3| = 19/3, which is a true statement so we can include B in our possible solutions. Check the box B.
Substitute C. x = -4/5 into the equation.
|(-4/5) + 3| = 4(-4/5) - 7
Solve as you did the other ones; add inside the absolute values and multiply and subtract 7 from the answer on the right side of the equation. After doing this you will get: 2.2 = -10.2, which is a false statement so C will be eliminated from possible answer choices.
Substitute the last one; D. x = -10/3.
|(-10/3) + 3| = 4(-10/3) - 7
Solving this you will end up with: 0.3 = -20.3, which is a false statement so the only answer choice that is a possible solution is B.
