Linear Equation Solver Calculator

Approach

Step 1

Step 1 - Set up the problem.

In this problem: The equation is \(2x + 3 = 11\), with \(2x + 3\) on the left of the equals sign and \(11\) on the right.

Step 2

Step 2 - Expand and simplify. Remove the brackets and combine the like terms on each side with a Simplifying of Algebraic Expressions.

In this problem: Neither \(2x + 3\) nor \(11\) has a bracket to remove or a pair of like terms to combine, so both sides are carried down unchanged.

Step 3

Step 3 - Collect the variable terms. Move every term that holds the variable onto one side by adding or subtracting that term on both sides, so the equation stays balanced.

In this problem: The right side is \(11\), which holds no \(x\) term, so every variable term already sits on the left and both sides are carried down unchanged.

Step 4

Step 4 - Collect the constant terms. Move every constant onto the other side by adding or subtracting that constant on both sides, so the equation stays balanced.

In this problem: The left side is \(2x + 3\), which still holds the constant \(3\).

Step 4a

Step 4a - Collect the constant terms. Move every constant onto the other side by adding or subtracting that constant on both sides, so the equation stays balanced.

In this problem: \(3\) is subtracted from both sides to clear that constant off the left.

Step 4b

Step 4b - Collect the constant terms. Move every constant onto the other side by adding or subtracting that constant on both sides, so the equation stays balanced.

In this problem: On the left, \(3 - 3 = 0\), so only the variable term is left there. On the right, \(11 - 3 = 8\).

Step 5

Step 5 - Isolate the variable. Undo the coefficient that is still attached to the variable, so the variable stands on its own.

In this problem: The left side is \(2x\), so \(x\) still carries the coefficient \(2\).

Step 5a

Step 5a - Isolate the variable. Undo the coefficient that is still attached to the variable, so the variable stands on its own.

In this problem: The coefficient \(2\) multiplies \(x\), and multiplying is undone by dividing, so both sides are divided by \(2\).

Step 5b

Step 5b - Isolate the variable. Undo the coefficient that is still attached to the variable, so the variable stands on its own.

In this problem: On the left, \(\frac{2x}{2} = x\). On the right, \(\frac{8}{2} = 4\).

Step 6

Step 6 - Verify the solution. Put the answer back into the original equation and check that both sides come out equal.

In this problem: Putting \(x = 4\) back into the original equation replaces every \(x\). The left side becomes \(2\left(4\right) + 3\), which works out to \(11\). The right side becomes \(11\), which works out to \(11\). Both sides give the same value, so the answer is correct.

Final Answer

Approach

Step 1

Step 1 - Set up the problem.

In this problem: The equation is \(3x - 5 = x + 7\), with \(3x - 5\) on the left of the equals sign and \(x + 7\) on the right.

Step 2

Step 2 - Expand and simplify. Remove the brackets and combine the like terms on each side with a Simplifying of Algebraic Expressions.

In this problem: Neither \(3x - 5\) nor \(x + 7\) has a bracket to remove or a pair of like terms to combine, so both sides are carried down unchanged.

Step 3

Step 3 - Collect the variable terms. Move every term that holds the variable onto one side by adding or subtracting that term on both sides, so the equation stays balanced.

In this problem: The left side holds \(3x\) and the right side holds \(x\), so a variable term is still sitting on the right.

Step 3a

Step 3a - Collect the variable terms. Move every term that holds the variable onto one side by adding or subtracting that term on both sides, so the equation stays balanced.

In this problem: To gather both variable terms on the left, \(x\) is subtracted from both sides.

Step 3b

Step 3b - Collect the variable terms. Move every term that holds the variable onto one side by adding or subtracting that term on both sides, so the equation stays balanced.

In this problem: On the left, \(3x - x = 2x\). On the right, \(x - x = 0\), so the right side no longer holds \(x\).

Step 4

Step 4 - Collect the constant terms. Move every constant onto the other side by adding or subtracting that constant on both sides, so the equation stays balanced.

In this problem: The left side is \(2x - 5\), which still holds the constant \(-5\).

Step 4a

Step 4a - Collect the constant terms. Move every constant onto the other side by adding or subtracting that constant on both sides, so the equation stays balanced.

In this problem: \(5\) is added to both sides to clear that constant off the left.

Step 4b

Step 4b - Collect the constant terms. Move every constant onto the other side by adding or subtracting that constant on both sides, so the equation stays balanced.

In this problem: On the left, \(-5 + 5 = 0\), so only the variable term is left there. On the right, \(7 + 5 = 12\).

Step 5

Step 5 - Isolate the variable. Undo the coefficient that is still attached to the variable, so the variable stands on its own.

In this problem: The left side is \(2x\), so \(x\) still carries the coefficient \(2\).

Step 5a

Step 5a - Isolate the variable. Undo the coefficient that is still attached to the variable, so the variable stands on its own.

In this problem: The coefficient \(2\) multiplies \(x\), and multiplying is undone by dividing, so both sides are divided by \(2\).

Step 5b

Step 5b - Isolate the variable. Undo the coefficient that is still attached to the variable, so the variable stands on its own.

In this problem: On the left, \(\frac{2x}{2} = x\). On the right, \(\frac{12}{2} = 6\).

Step 6

Step 6 - Verify the solution. Put the answer back into the original equation and check that both sides come out equal.

In this problem: Putting \(x = 6\) back into the original equation replaces every \(x\). The left side becomes \(3\left(6\right) - 5\), which works out to \(13\). The right side becomes \(\left(6\right) + 7\), which works out to \(13\). Both sides give the same value, so the answer is correct.

Final Answer