Question

order of operations arithmetic sequences directions: write an expression and then choose a value for x that would make the expression true. 12 less than 4 times a number is the same as -2 times the number. a. x = 2 b. x = -2 c. x = -3

Explanation:

Step1: Define the variable and translate the problem into an equation.

Let the number be \( x \). "12 less than 4 times a number" can be written as \( 4x - 12 \), and "-2 times the number" is \( -2x \). So the equation is \( 4x - 12 = -2x \).

Step2: Solve the equation for \( x \).

Add \( 2x \) to both sides of the equation: \( 4x + 2x - 12 = -2x + 2x \), which simplifies to \( 6x - 12 = 0 \). Then add 12 to both sides: \( 6x - 12 + 12 = 0 + 12 \), so \( 6x = 12 \). Divide both sides by 6: \( x=\frac{12}{6}=2 \)? Wait, no, wait, let's check the options. Wait, maybe I made a mistake. Wait, let's substitute the options into the original expression.

Step3: Substitute option a (\( x = 2 \)) into the left - hand side (LHS) and right - hand side (RHS) of the expression.

LHS: 4 times 2 minus 12 is \( 4\times2 - 12=8 - 12=-4 \). RHS: - 2 times 2 is \( - 4 \). So LHS = RHS when \( x = 2 \). Wait, but let's check option b: \( x=-2 \). LHS: \( 4\times(-2)-12=-8 - 12=-20 \). RHS: \( -2\times(-2) = 4 \). Not equal. Option c: \( x = - 3 \). LHS: \( 4\times(-3)-12=-12 - 12=-24 \). RHS: \( -2\times(-3)=6 \). Not equal. Wait, but according to the equation \( 4x-12=-2x \), solving it: \( 4x + 2x=12 \), \( 6x = 12 \), \( x = 2 \). So the correct option is a.

Answer:

a. \( x = 2 \)