Question

math 6 notes (8.1)
name
solving one - step equations - addition/subtraction

• an equation is a math sentence that does contain an
• the goal of solving an equation is to find the value of the variable.
• we do this by isolating the variable on one side of the equation using inverse operations!
• inverse operations “undo” each other!

inverse of addition?
inverse of subtraction?
inverse of multiplication?
inverse of division?
examples:
john has x apples. if he adds 5 apples to his pile, he will have 8 apples.
what is the value of x?
write an equation: $x + 5 = 8$
$\underline{\quad - 5 = - 5\quad}$
$x = 3$
answer: john had 3 apples before he added to his pile.
check: $3 + 5 = 8$
maddie has x dollars. after spending $90 on a purse, she will have $45. what is the value of x?
write an equation: $x - 90 = 45$
$\underline{\quad + 90 = + 90\quad}$
$x = 135$
answer: maddie had $135 before she bought the purse.
check: $135 - 90 = 45$
let’s practice!

1. $x + 2 = 10$

$\underline{\quad\square\quad\square\quad}$
$x + 0 = \square$
check:

1. $y - 8 = 15$

$\underline{\quad\square\quad\square\quad}$
$y - 0 = \square$
check:

1. $a + 9 = 2$

$\underline{\quad\square\quad\square\quad}$
$a + 0 = \square$
check:

Explanation:

Problem 1: \( x + 2 = 10 \)

Step1: Use inverse of addition (subtraction)

To isolate \( x \), subtract 2 from both sides of the equation:
\( x + 2 - 2 = 10 - 2 \)

Step2: Simplify both sides

Simplify the left side (\( x + 0 = x \)) and the right side (\( 10 - 2 = 8 \)):
\( x = 8 \)

Check:

Substitute \( x = 8 \) back into the original equation:
\( 8 + 2 = 10 \), which is true.

Problem 2: \( y - 8 = 15 \)

Step1: Use inverse of subtraction (addition)

To isolate \( y \), add 8 to both sides of the equation:
\( y - 8 + 8 = 15 + 8 \)

Step2: Simplify both sides

Simplify the left side (\( y - 0 = y \)) and the right side (\( 15 + 8 = 23 \)):
\( y = 23 \)

Check:

Substitute \( y = 23 \) back into the original equation:
\( 23 - 8 = 15 \), which is true.

Problem 3: \( a + 9 = 2 \)

Step1: Use inverse of addition (subtraction)

To isolate \( a \), subtract 9 from both sides of the equation:
\( a + 9 - 9 = 2 - 9 \)

Step2: Simplify both sides

Simplify the left side (\( a + 0 = a \)) and the right side (\( 2 - 9 = -7 \)):
\( a = -7 \)

Check:

Substitute \( a = -7 \) back into the original equation:
\( -7 + 9 = 2 \), which is true (since \( -7 + 9 = 2 \)).

Answer:

s:

1. \( x = \boldsymbol{8} \)
2. \( y = \boldsymbol{23} \)
3. \( a = \boldsymbol{-7} \)