# Equations as Sentences

## Equations on the grid

For each value of \$x\$ in the table below, slide the slider to find the value of \$4x-2\$.

\$x\$\$4x-2\$
 Look at the table from firstExp. In the row of that table where \$4x-2=10\$, what number does \$x\$ equal?
 There are \$2x+3\$ green squares on the grid. Slide the slider to find the value of \$x\$ which makes \$2x+3=5\$.

A mathematical sentence with an equals sign, like \$3x+5=11\$, is called an equation. An equation may be true or false, depending on the value of \$x\$. To solve an equation means to find the value(s) of \$x\$ which make it true. Those values are the equation’s solutions.

 Slide the slider for the grid to the left to solve the equation \$3x+5=11\$.
 The height of the rectangle on the grid is \$\$12/x\$\$. Slide the slider to make the rectangle have height \$3\$ and solve the equation \$\$12/x=3\$\$.

## Equations for word problems

The Mathscribe Fruit Stand sells apples for \\$2 each, so if you want to buy \$a\$ apples, the number of dollars it will cost is \$2a\$.

 If you have \\$14 to spend on apples, you can solve the equation \$2a=14\$ to find the number of apples you can buy. Slide the slider to solve this equation.
 If you have \\$8 to spend on apples, what is an equation that tells you how many apples you can buy?
 Solve that equation.
 A basket costs \\$8 at the Mathscribe Fruit Stand, and apples still cost \\$2. If you have \\$18, and you want to buy \$a\$ apples and a basket to put them in, an equation for the number of apples you can buy is \$2a+8=18\$. Slide the slider to solve the equation and find the number of apples you can buy.