Equations & Inequalities

6.F.1One-step equations01/04

Solve one-step equations.

Step01of 04

To solve an equation, isolate the variable using the OPPOSITE operation. Whatever you do to one side, do to the other.

Addition equation	→ $x + 7 = 12$ → subtract 7
Subtraction	→ $x - 4 = 9$ → add 4
Multiplication	→ $5 x = 30$ → divide by 5
Division	→ $x /3 = 8$ → multiply by 3

6.F.1 — Solve one-step equations.

Step 01 of 04

To solve an equation, isolate the variable using the OPPOSITE operation. Whatever you do to one side, do to the other.

Addition equation	→ $x + 7 = 12$ → subtract 7
Subtraction	→ $x - 4 = 9$ → add 4
Multiplication	→ $5 x = 30$ → divide by 5
Division	→ $x /3 = 8$ → multiply by 3

Step 02 of 04

Worked example. $x + 7 = 12$ .

x + 7 - 7 = 12 - 7

x = 5

Check: $5 + 7 = 12$ $✓$ .

Step 03 of 04

Multiplication and division.

5 x = 30 \Rightarrow x = 6

x /3 = 8 \Rightarrow x = 24

Step 04 of 04

Word problem. Sara saved $14 more than her brother. Sara has $35. How much does her brother have?

b + 14 = 35 \Rightarrow b = $21

Key insight

Use the OPPOSITE operation to undo what's happening to the variable. Apply to BOTH sides. Always check by plugging in.

6.F.2 — Independent vs. dependent variables.

Step 01 of 04

In an equation with two variables, one is INDEPENDENT (you choose its value) and one is DEPENDENT (its value depends on the first).

Step 02 of 04

Example. A car travels at 50 mph. After $t$ hours, distance traveled is $d = 50 t$ .

t (independent)	→time — you choose how many hours
d (dependent)	→distance — depends on t

Step 03 of 04

Make a table.

t = 1	→d = 50
t = 2	→d = 100
t = 3	→d = 150
t = 4	→d = 200

Step 04 of 04

Graph: independent on x-axis, dependent on y-axis. Plot (1, 50), (2, 100), (3, 150). The line shows how distance grows with time.

Key insight

Independent = chosen / cause. Dependent = response / effect. By convention, x-axis = independent, y-axis = dependent. Tables and graphs make the relationship visible.

6.F.3 — Write and graph one-variable inequalities.

Step 01 of 04

Inequality symbols.

$<$	→less than
$>$	→greater than
$\leq$	→less than or equal
$\geq$	→greater than or equal

Step 02 of 04

Translate words.

"x is at least 5"	→ $x \geq 5$
"y is at most 10"	→ $y \leq 10$
"more than 7"	→ $> 7$
"no more than 12"	→ $\leq 12$

Step 03 of 04

Graph on a number line.

$x > 5$	→OPEN dot at 5, ARROW going right
$x \geq 5$	→CLOSED dot at 5, ARROW going right
$x < 5$	→OPEN dot at 5, arrow LEFT
$x \leq 5$	→CLOSED dot at 5, arrow LEFT

Step 04 of 04

Open dot = endpoint NOT included (strict $<$ / $>$ ). Closed dot = endpoint included ( $\leq$ / $\geq$ ). The arrow shows infinitely many solutions in that direction.

Key insight

Inequalities allow MANY solutions, not one. Open dot = strict; closed dot = inclusive. Arrow shows the infinite range of solutions.

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6.F.1 – 6.F.3 · CCSS 6.EE.B / 6.EE.C · Full curriculum →