Lesson 1.1: Solving One & Two Step Equations

Flashcards covering concepts, definitions, rules of equality, operation key terms, and solved examples from Lesson 1.1 on Solving One & Two Step Equations.

What is the definition of an equation?

A mathematical sentence that contains an equal sign between two equivalent expressions.

What is the definition of a solution to an equation?

A value of an equation that makes the equation true.

What are inverse operations?

Operations that undo each other.

What condition must be met to solve an equation for a variable?

The variable must be isolated on one side of the equation.

What is the Subtraction Property of Equality?

For any numbers $a$, $b$, and $c$, if $a = b$, then $a - c = b - c$.

What is the Addition Property of Equality?

For any numbers $a$, $b$, and $c$, if $a = b$, then $a + c = b + c$.

What is the Multiplication Property of Equality?

For any numbers $a$, $b$, and $c$, if $a = b$, then $ac = bc$.

What is the Division Property of Equality?

For any numbers $a$, $b$, and $c$, if $a = b$, then $\frac{a}{c} = \frac{b}{c}$.

Which key terms indicate addition in mathematical word problems?

plus, sum, increased by, more than

Which key terms indicate subtraction in mathematical word problems?

minus, difference, decreased by, less than

Which key terms indicate multiplication in mathematical word problems?

times, product, of, double, triple, etc.

Which key terms indicate division in mathematical word problems?

divided by, quotient, goes into, per

Which key terms indicate an equals sign in mathematical word problems?

is equal to, is

Is $10$ the solution to $3y - 1 = 32$?

No, because $3(10) - 1 = 29 \neq 32$.

Is $-8$ the solution to $\frac{x}{2} + 6 = 2$?

Yes, because $\frac{-8}{2} + 6 = -4 + 6 = 2$.

Is $5$ the solution to $4p + 3 = 17$?

No, because $4(5) + 3 = 23 \neq 17$.

Is $24$ the solution to $\frac{x}{6} + 7 = 11$?

Yes, because $\frac{24}{6} + 7 = 4 + 7 = 11$.

What is the solution to $x - 6 = 22$?

$$x = 28$$

What is the solution to $7x = 77$?

$$x = 11$$

What is the solution to $x + 10 = -7$?

$$x = -17$$

What is the solution to $\frac{x}{5} = 21$?

$$x = 105$$

What is the solution to $8x - 3 = 85$?

$$x = 11$$

What is the solution to $-34 = 6 - 4x$?

$$x = 10$$

What is the solution to $\frac{x}{5} + 11 = 17$?

$$x = 30$$

What equation corresponds to "Eight more than 3 times a number is 29", and what is its solution?

The equation is $3x + 8 = 29$, and the solution is $x = 7$.

What equation corresponds to "Ten less than six times a number is eight", and what is its solution?

The equation is $6x - 10 = 8$, and the solution is $x = 3$.