Linear Equations Flashcards

All 7 cards in this deck

What are the steps to solve a multi-step linear equation with the unknown on one side?

e.g. $4x + 7 = 19$

1. Undo the $+7$: subtract 7 from both sides $\rightarrow 4x = 12$
2. Undo the $\times 4$: divide both sides by 4 $\rightarrow x = 3$

What are the steps to solve a linear equation with the unknown on both sides?

e.g. $5x - 14 = 52 - x$

1. Add $x$ to both sides to collect $x$ terms on one side: $6x - 14 = 52$
2. Add 14 to both sides: $6x = 66$
3. Divide both sides by 6: $x = 11$

True or false? To solve $2(x+5) = 16$ you are allowed to divide both sides by 2 instead of expanding the bracket.

True.
Dividing both sides by 2 gives $x + 5 = 8$, so $x = 3$ — the same answer as expanding first.

What are the steps to solve a linear equation containing numerical denominators?

e.g. $\frac{x+1}{4} + \frac{x}{3} = 2$

1. Multiply every term by the lowest common denominator (12): $3(x+1) + 4x = 24$
2. Expand and collect terms: $7x + 3 = 24$, so $7x = 21$
3. Divide both sides by 7: $x = 3$

How do you use a graph to find an approximate solution of a linear equation?

e.g. use the graph of $y = 2x + 3$ to solve $2x + 3 = 6$

Draw the line $y = 6$ and read off the $x$-coordinate where the two lines cross.
Here $x = 1.5$.

After solving the equation in a worded or measurement problem, what must you still do?

e.g. shelf B holds $(3x+1)$ books and you have found $x = 8$

Substitute the value of $x$ back into the expression the question asks about, and state the units.
Here $3 \times 8 + 1 = 25$ books.

True or false? The solution of $3x - 12 = 0$ is read off the graph of $y = 3x - 12$ at the $y$-intercept.

False. It is the $x$-coordinate of the point where the line crosses the $x$-axis.