Solving Equations Review

Multiply each term inside the parentheses by $$\frac{1}{3}$$ : 1. $$\frac{1}{3} \cdot 6x = 2x$$ 2. $$\frac{1}{3} \cdot 9y = 3y$$ 3. $$\frac{1}{3} \cdot -15 = -5$$ Final result: $$2x + 3y - 5$$ .

The equation is: $$30 - x = 40 - 2x$$ .

The equation is: $$300 + 250m = 400m$$ , where m is the time in minutes.

1. Distribute -4: $$12 = 24x + 12$$ 2. Subtract 12 from both sides: $$0 = 24x$$ 3. Divide by 24: $$x = 0$$ .

Multiply both sides by 5 to eliminate the fraction: $$x + 6 = 50$$ .

A variable is a symbol (often a letter) that represents an unknown value in mathematical expressions or equations.

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

The distributive property states that $$a(b + c) = ab + ac$$ , meaning you can distribute a factor across a sum.

Subtract 5 from both sides: $$x = 12 - 5 = 7$$ .

Substitute the solution back into the original equation to see if both sides are equal.