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.

What would the equation be if you had \$12 instead?

A teacher has $20$ cookies to divide among her students. She wants to give them out as a prize to the first $s$ students to come to class. If each student gets $4$ cookies, an equation for the number of students who get a prize is $$20/s = 4$$.

Slide the slider to solve this equation.

If the teacher had $24$ cookies instead, what would the equation be?