Equations for 7th grade - Examples, Exercises and Solutions

To solve this exercise, we first need to identify that we have an equation with an unknown,

To solve such equations, the first step will be to arrange the equation so that on one side we have the numbers and on the other side the unknowns.

$2X+7-5X-12=-8X+3$

First, we'll move all unknowns to one side.
It's important to remember that when moving terms, the sign of the number changes (from negative to positive or vice versa).

$2X+7-5X-12+8X=3$

Now we'll do the same thing with the regular numbers.

$2X-5X+8X=3-7+12$

In the next step, we'll calculate the numbers according to the addition and subtraction signs.

$2X-5X=-3X$
$-3X+8X=5X$

$3-7=-4$$$
$-4+12=8$

$5X=8$

At this stage, we want to get to a state where we have only one $X$, not $5X$,
so we'll divide both sides of the equation by the coefficient of the unknown (in this case - 5).

$X={8\over5}$

Let's solve the given equation, noting that on the right side of the given equation is the number 0, and on the left side is a multiplication of algebraic expressions only:

$5x(x+2)(x+5)= 0$From here we'll remember that the result of multiplication between expressions will yield 0 only if at least one of the multiplying expressions equals zero,

Therefore we'll get three simple equations and solve them by isolating the variable in each:

$\boxed{x=0}$or:

$x+2=0\\ \boxed{x=-2}$

or:

$x+5=0\\ \boxed{x=-5}$

Therefore the correct answer is answer D.