Question

Solve and check , -0.7+2.8=-3.14x-5.2 I need to see the work because I’m super confused

Answer 1

In order to solve equations like these, you need to move all terms involving the variable on one side, and all the numeric constants on the other side.

To do so, we can add/subtract the same quantity to both sides.

For example, we can add 5.2 to both sides to get

$-0.7+2.8+5.2=-3.14x-5.2+5.2 \iff -0.7+2.8+5.2=-3.14x$

Then, we can add all the terms on the left hand side, and we have

$-0.7+2.8+5.2=-3.14x \iff 7.3=-3.14x$

Finally, we can divide both sides by -3.14:

$\dfrac{7.3}{-3.14} = \dfrac{-3.14x}{-3.14} \iff x = -\dfrac{7.3}{3.14}$

In order to check the solution, we have to plug the value we found for x in the initial equation:

$-0.7+2.8=-3.14x-5.2 \iff -0.7+2.8=-3.14\cdot \left(-\dfrac{7.3}{3.14}\right) -5.2 \iff -0.7+2.8 = 7.3-5.2 \iff 2.1=2.1$

which is clearly true.