Solve equations with the unknown on both sides (negative numbers and fractions). Plot straight lines on a graph, including parallel and perpendicular lines. Solve equations with th... Solve equations with the unknown on both sides (negative numbers and fractions). Plot straight lines on a graph, including parallel and perpendicular lines. Solve equations with the unknown on both sides graphically. Form and solve equations from words. Form and solve equations in geometric contexts. Simplify and manipulate algebraic fractions. Solve linear equations with algebraic fractions. Rearrange equations with the subject of the formula on both sides. Read more

Steps to Solve

1. Identify the Key Areas to Review Before starting, we need to identify what specific areas we want to focus on: solving equations, graphing lines, or handling algebraic fractions.

2. Solving Equations with Unknowns on Both Sides Start with an equation such as $3x + 2 = x + 10$. To solve for $x$, first, eliminate $x$ from one side. Subtract $x$ from both sides: $$ 3x - x + 2 = 10 $$ This simplifies to: $$ 2x + 2 = 10 $$

3. Isolate the Variable Next, subtract 2 from both sides: $$ 2x = 8 $$ Now divide both sides by 2 to find $x$: $$ x = 4 $$

4. Plotting a Straight Line For graphing, you might start with the equation $y = 2x + 1$. To plot, find two points. For $x = 0$, $y = 1$. For $x = 1$, $y = 3$. These points $(0, 1)$ and $(1, 3)$ can be plotted on a graph to draw the line.

5. Solving Equations Graphically To solve an equation like $y = x + 1$ and $y = 2x - 2$ graphically, plot both lines on the same graph. The point where they intersect gives the solution.

6. Simplifying Algebraic Fractions If dealing with an algebraic fraction like $\frac{x + 2}{x - 3}$, start by checking for restrictions (in this case, $x \neq 3$).

7. Combine Fractions if Necessary If you have $\frac{x}{x-3} + \frac{2}{x-3}$, combine them: $$ \frac{x + 2}{x - 3} $$

8. Factor if Possible If necessary, try to factor to simplify your final expression.