Linear equations

• What is a linear equation?

  A linear equation is an equation that will produce a straight line when plotted on a graph.
• What is the greatest power of x in a linear equation?

  The greatest power of x in a linear equation is 1.

  
• What does it mean if a linear equation has no terms of x² or higher order?

  It means that the equation is linear and only involves the first power of x.

  
• What is the standard form of a linear equation?

  A linear equation is normally in the form $ax +$$b =$$c$.

  
• What is the process to solve a linear equation?

  To solve a linear equation, you need to isolate the variable by carrying out inverse operations to both sides of the equation.

  
• What are inverse operations?

  Inverse operations are the opposite operations to what has already happened to the variable.
• Why is the order of inverse operations important when solving linear equations?

  The order in which the inverse operations are carried out is important to correctly isolate the variable.

  
• What does BIDMAS stand for?

  BIDMAS stands for Brackets, Indices, Division and Multiplication, Addition and Subtraction.
• How do you solve the equation $2x +$$1 =$$9$?


  Subtract 1 to get $2x =$$8$, then divide by 2 to find $x =$$4$.
• What is the first step to solve the equation $2 - 3x =$$10$?


  The first step is to subtract 2 to get $-3x =$$8$.

  
• What should you be careful about when solving equations with negative terms?

  You should be careful not to drop the negative sign on coefficients.

  
• How do you solve a linear equation with the unknown variable on both sides?

  Start by collecting the terms with the variable on one side of the equation.

  
• What is the easiest way to move the x term when solving equations with variables on both sides?

  Moving the x term with the smallest coefficient is easiest.

  
• How do you solve the equation $4x - 7 =$$11 +$$x$?


  Move the x term with the smallest coefficient to get $3x - 7 =$$11$, then solve to find $x =$$6$.

  
• What should you do if a linear equation contains brackets?


  Start by expanding the brackets on one or both sides of the equation.
• How do you solve the equation $2(x - 1) =$$10 - (3 + x)$?


  Expand the brackets to get $2x - 2 =$$10 - 3 - x$, then solve.

  
• What is the first step to solve the equation $3x - 2 =$$7 - x$?


  Expand the brackets and then collect the x terms to one side.

  
• How do you solve a linear equation that contains fractions?

  Remove the fractions by multiplying both sides by everything on the denominator.

  
• What should you remember when multiplying both sides of an equation by the denominator?

  Remember to put brackets around the expression.

  
• How do you solve the equation $\frac{2}{x + 3} =$$\frac{3}{4 - 2x}$?


  Multiply both sides by $(x + 3)(4 - 2x)$ to eliminate the fractions.

  
• What is the next step after expanding the brackets in the equation $8 - 4x =$$3x +$$9$?


  Collect the x terms to one side by subtracting the term with the smaller coefficient of x.

  
• How do you solve the equation $7x +$$9 =$$8$?


  Subtract 9 from both sides to get $7x =$$-1$, then divide by 7 to find $x =$$-\frac{1}{7}$.

  
• What should you do if you have time in the exam after solving an equation?

  You should substitute your answer back into the equation to check you got it right.
• What are the steps to solve a linear equation?

  1. Identify the operations applied to the variable.
  2. Carry out the inverse operations in reverse order.
  3. Isolate the variable.
  4. Check your solution by substituting back into the original equation.

  
• What are the steps to solve a linear equation that contains brackets?

  1. Expand the brackets on both sides.
  2. Collect the x terms to one side.
  3. Solve the resulting linear equation.

  
• What are the steps to solve a linear equation that contains fractions?

  1. Remove the fractions by multiplying both sides by the denominator.
  2. Expand the brackets if necessary.
  3. Collect the x terms to one side.
  4. Solve the resulting linear equation.

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

  1. Collect the terms with the variable on one side.
  2. Isolate the variable by performing inverse operations.
  3. Solve the resulting linear equation.