Solve for x: 4x + 7 = 23.

• A. 4
• B. 5
• C. 3
• D. 6

Answer: (A)

Solving a linear equation by isolating the variable means undoing the operations that involve the variable until it stands alone. Here, x is multiplied by four and then increased by seven to reach twenty-three. To undo that, first subtract seven from both sides, which leaves four times x on the left and sixteen on the right. Next, divide both sides by four to undo the multiplication, giving x equals four. Check by substitution: four times four plus seven equals sixteen plus seven, which is twenty-three, so it matches the right side. Therefore, the value that satisfies the equation is four. If x were five, the left side would be twenty-seven; if x were three, it would be nineteen; if x were six, it would be thirty-one—none of these equal twenty-three.