What are math equations?

Math equations are statements made up of algebraic expressions and an equal sign. Math equations include defined math formulas that can be solved with substitution.

• Math formulas are rules that connect two or more variables. They are used to work out the values of unknown variables by substituting in other known values.

For example, here is a rectangle with base $b$ and height $h.$

The area of any rectangle can be found with the formula $b \times h.$

• Substitution is when you give variables in an algebraic expression, equation or inequality a value. You use substitution to identify solutions.

For example,

Does $x = 2$ make the equation $5x+2=14$ true?

Substitute $2$ for $x$ and follow the order of operations:

$5 \times 2+2=14$

$10+2=14$

$12$ ≠ $14$

Substituting $2$ for $x,$ does not make the equation true, so $2$ is not a solution of the equation $5x+2=14.$

Step-by-step guide:

• Math equations also include multi step equations and equations with fractions.

One step equations are algebraic equations with a single variable that can be solved with one step.

In order to solve, you will need to isolate the variable (get it alone) on one side of the equation. This can be done with a model or by using the inverse operation.

For example, $3x =15$

Using a model:

Using inverse operations:

Sort the $(+1)$ tiles so an equal amount are with each $(x)$ tile. There are five $(+1)$ tiles for each $(x)$ tile. $x=5$

$3x=15$ Get the variable alone by using the inverse operation. The inverse operation of multiplication is division. Divide $3$ on both sides of the equation. $\cfrac{3x}{3}=\cfrac{15}{3}$ Since $\cfrac{3}{3} \,=1,$ the left side can be written as $1x$ or $x.$ The right side of the equation can be written as $\cfrac{15}{3}=5.$ $x=5$ You can check your answer by substituting the value for $x$ into the original equation. $\begin{aligned} 3x&=15\\ 3(5)&=15 \; \color{#77dd77} ✔ \end{aligned}$

Step-by-step guide: One step equations

• Solving equations with fractions is when the unknown is part of the numerator and/or denominator of a fraction.

To solve equations with fractions, apply the inverse operation to both sides of the equation – a strategy also referred to as the “balance method.”

The inverse operation of division is multiplication.

For example, $\, \cfrac{x+3}{3}=8$

$3\left(\cfrac{x+3}{3}\right)=3(8) \quad$ *Multiply each side by $3.$

$x+3=24$

$-3 \quad \; -3 \quad$ *Subtract $3$ from both sides.

$x = 21$

Check your work by substituting the answer into the equation.