Rearranging equations

How to Solve an Algebra Problem

1. Step 1: Write Down the Problem.
2. Step 2: PEMDAS.
3. Step 3: Solve the Parenthesis.
4. Step 4: Handle the Exponents/ Square Roots.
5. Step 5: Multiply.
6. Step 6: Divide.
7. Step 7: Add/ Subtract (aka, Combine Like Terms)
8. Step 8: Find X by Division.

The order of operations is Parenthesis, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This can be remembered in two ways: “Please Excuse My Dear Aunt Sally” or PEMDAS.

RULE #1: you can add, subtract, multiply and divide by anything, as long as you do the same thing to both sides of the equals sign. and rearrange it. We want to isolate the variable for mass (m).

Rearranging formulae In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject. Knowledge of solving equations and inverse operations is very useful.

1. For example,
2. To rearrange the equation so that it is written as take each term and move to the other side of the equal sign using the opposite operation until you only have.
3. e.g. Rearrange to make the subject of the equation.
4. Take to the other side of the equal sign by adding to both sides.

Speed is calculated using the formula S= D T where S = speed, D = distance, and T = time. Rearrange the formula to solve for time (T). Speed is calculated using the formula S= D/T where S = speed, D = distance, and T = time.

The basic technique to isolate a variable is to “do something to both sides” of the equation, such as add, subtract, multiply, or divide both sides of the equation by the same number. By repeating this process, we can get the variable isolated on one side of the equation.

The keep to isolating variables is to get every multiple or quotient with that variable on one side of the equal side and everything without that variable on the other side. Finally, combine any terms that aren’t already combined, and get rid of the coefficient of the variable, if there is one.

Answer and Explanation: Rewriting literal equations is useful in mathematical applications, because in doing so, we can isolate a specific variable on one side of the…

Generally, when solving equations of this type for a specific quantity, you first make sure that quantity is “upstairs” (“flip” if it isn’t). Then divide both sides of the equation by what is necessary to get the quantity of interest on one side of the equation by itself.

Terms in this set (5)

• Literal Equation. An equation that has more than one variable.
• Formula. The most common type of literal equation.
• A=bh/2. An example of a formula (this is the formula for area of a rectangle)
• In formulas.
• To solve for x.

A literal equation is one that has several letters or variables. Examples include the area of a circle (A=πr2) and the formula for speed (v=Dt). If the unknown variable is in the denominator, we multiply both sides by the lowest common denominator (LCD) and then continue to solve.

The general procedure for solving multi-step inequalities is as follows.

1. Clear parentheses on both sides of the inequality and collect like terms.
2. Add or subtract terms so the variable is on one side and the constant is on the other side of the inequality sign.

How to solve a formula with variables for a specified variable?

1. Solve for r. d = rt.
2. Solve for h. A = 1/2 bh.
3. Solve for b2 A = 1/2(b1 + b2)
4. Solve for w. P = 2L + 2W.
5. Write y in terms of x. y – 3 = 1/3(x – 4)
6. Solve for a.

To figure out if an ordered pair is a solution to an equation, you could perform a test. Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.

If the equation is in the form, ax + b = c, where x is the variable, you can solve the equation as before. First “undo” the addition and subtraction, and then “undo” the multiplication and division. Solve 3y + 2 = 11. Subtract 2 from both sides of the equation to get the term with the variable by itself.

Do unto one side of the equation, what you do to the other! An equation is like a balance scale. If we put something on, or take something off of one side, the scale (or equation) is unbalanced. When solving math equations, we must always keep the ‘scale’ (or equation) balanced so that both sides are ALWAYS equal.

We have 4 ways of solving one-step equations: Adding, Substracting, multiplication and division.

Solving Equations with a Variable on Both Sides. After simplifying, the first step in solving an equation with a variable on both sides is to get the variable on one side. This is done by reversing the addition or subtraction of one of the terms with the variable.

A two-step equation is an algebraic equation that takes you two steps to solve. You’ve solved the equation when you get the variable by itself, with no numbers in front of it, on one side of the equal sign.

In an equation, the quantities on both sides of the equal sign are equal. That’s the mathematical meaning of equation, but equation can also be used in any number of situations, challenges, or efforts to solve a problem.

• The Reflexive Property. a =a.
• The Symmetric Property. If a=b, then b=a.
• The Transitive Property. If a=b and b=c, then a=c.
• The Substitution Property. If a=b, then a can be substituted for b in any equation.
• The Addition and Subtraction Properties.
• The Multiplication Properties.
• The Division Properties.
• The Square Roots Property*