Question

Solve: 6x² = 7x. Enter an exact answer or round your answer to the nearest tenth.

A) x = 0.9
B) x = 1.2
C) x = 1.5
D) x = 1.7

Answer 1

To solve the equation 6x² = 7x, factor out x to get x(6x - 7) = 0. This yields two solutions: x = 0 and x = 7/6. The latter solution rounds to x = 1.2, matching answer choice B).

Step-by-step explanation:

To solve the equation 6x² = 7x, let's first set the equation to zero by moving all terms to one side:

6x² - 7x = 0

This is a quadratic equation, and we can begin solving it by factoring out an x:

x(6x - 7) = 0

This gives us two potential solutions when we set each factor equal to zero:

• x = 0
• 6x - 7 = 0 –> x = 7/6

From here, we can see that x has two possible values. To determine which ones are correct, we look at the answer choices:

1. x = 0.9
2. x = 1.2
3. x = 1.5
4. x = 1.7

Given our exact answers, we notice that x = 7/6 simplifies to approximately 1.2 when rounded to the nearest tenth, which matches choice B). Therefore, the correct answer to the equation 6x² = 7x is x = 1.2.