Question

Solve the equation for the given variable then place the equations in the table under the correct solution.

-14x = -42
-3 / 5 + x = 12 / 5
x - 5 = -2
-6 + x = -9
x/4 = 6/8x/3 = 9
a. x=3, x=2, x=3,x=−3, x=6, x=27.
b. x=−3, x=3, x=−3, x=−3, x=6, x=9.
c. x=3, x=3, x=3, x=−3, x=6, x=9.
d. x=3, x=−3, x=3, x=−3, x=6, x=9.

Answer 1

To solve the given equations, we isolate x by simplifying the equations and performing appropriate operations. The solutions are: x ≈ 3.21, x ≈ -2.33, x = -1.5, and x = 27.

Step-by-step explanation:

To solve the equation -14x = -42-3, we need to isolate x. First, simplify both sides of the equation by combining like terms: -14x = -45. Next, divide both sides by -14 to solve for x: x = -45 / -14. This simplifies to x = 45 / 14, or x ≈ 3.21.

For the equation -3 / 5 + x = 12 / 5x, we'll start by getting rid of the fractions. Multiply every term by 5x to eliminate the denominators: -3x + 5 = 12. Next, move the constant term to the right by subtracting 5 from both sides: -3x = 7. Finally, divide both sides by -3 to solve for x: x = 7 / -3, or x ≈ -2.33.

For the equation 5x - 5 = -2-6 + x = -9, we can simplify this to 4x - 5 = -11. Add 5 to both sides to isolate x: 4x = -6. Divide both sides by 4 to solve for x: x = -6 / 4, or x = -1.5.

Finally, for the equation x/3 = 9, we'll multiply both sides by 3 to get rid of the fraction: x = 9 * 3, which simplifies to x = 27.