How do you solve $$ \frac{4}{5}(x - 2) = 16 $$ ?

Multiply both sides by $$\frac{5}{4}$$ to get $$x - 2 = 20$$ . Then add 2 to both sides to find $$x = 22$$ .

How do you solve $$ \frac{3y + 9}{3} = 7 $$ ?

Multiply both sides by 3 to get $$3y + 9 = 21$$ . Then subtract 9 from both sides to find $$3y = 12$$ , and divide by 3 to get $$y = 4$$ .

What is the solution to the equation $$-5(x + 2) = -2(x + 2)$$ ?

Distributing gives $$-5x - 10 = -2x - 4$$ . Adding 5x to both sides and simplifying leads to $$-10 = 3x - 4$$ , so $$x = 0$$ .

What does it mean for an equation to have no solution?

An equation has no solution when the variables cancel out and you are left with a false statement, such as $$0 = 5$$ .

What is the solution to $$-12(x - 1) = -3(x - 1)$$ ?

Distributing gives $$-12x + 12 = -3x + 3$$ . Adding 12x to both sides leads to $$12 = 9x + 3$$ , so $$x = 1$$ .

What is the importance of checking your solution?

Checking your solution involves substituting it back into the original equation to ensure it satisfies the equation, confirming that your solution is correct.

What is a coefficient in an equation?

A coefficient is a numerical factor that multiplies a variable in an equation, such as the 4 in $$4x$$ .

What is the difference between an equation and an expression?

An equation states that two expressions are equal, while an expression is a combination of numbers, variables, and operations without an equality sign.

Solving Linear Equations Practice One Flashcard

Student preview

14 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a linear equation?

Back

2.

FLASHCARD QUESTION

Front

How do you isolate a variable in an equation?

Back

3.

FLASHCARD QUESTION

Front

What does it mean to solve for x?

Back

Solving for x means finding the value of x that makes the equation true. This involves manipulating the equation to isolate x.

4.

FLASHCARD QUESTION

Front

What is the distributive property?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the perimeter of a rectangle?

Back

7.

FLASHCARD QUESTION

Front

How do you express width in terms of perimeter and length?

Back

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