In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle \frac{x}{5}+9=-10\)

Subtract \(\displaystyle 9\) from both sides of the equation.

\(\displaystyle \frac{x}{5}+9-9=-10-9\)

When subtracting a negative number from another negative number, we will treat it as an addition problem and then add a negative sign to the sum.

\(\displaystyle \frac{x}{5}=-(10+9)\)

Simplify.

\(\displaystyle \frac{x}{5}=-19\) 

Multiply both sides of the equation by \(\displaystyle 5\). 

\(\displaystyle (5)\frac{x}{5}=-19(5)\)

Solve. When multiplying a negative number by a positive number, our answer is negative.

\(\displaystyle x=-95\)

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle 6x-9=111\) 

Add \(\displaystyle 9\) to both sides of the equation.
\(\displaystyle 6x-9+9=111+9\)

Simplify.

\(\displaystyle 6x=120\) 

Divide both sides of the equation by \(\displaystyle 6\).

\(\displaystyle \frac{6x}{6}=\frac{120}{6}\)

Solve.

\(\displaystyle x=20\)

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle 7x-19=-47\) 

Add \(\displaystyle 19\) to both sides of the equation.

\(\displaystyle 7x-19+19=-47+19\)

Remember since \(\displaystyle 47\) is greater than \(\displaystyle 19\) and is negative, our answer is negative. We will treat this operation as a subtraction problem.

\(\displaystyle 7x=-(47-19)\)

Simplify.

\(\displaystyle 7x=-28\) 

Divide both sides of the equation by \(\displaystyle 7\).

\(\displaystyle \frac{7x}{7}=\frac{-28}{7}\)

Solve. When dividing a negative number with a positive number, our answer becomes negative.

\(\displaystyle x=-4\)

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle -4x-19=21\) 

Add \(\displaystyle 19\) to both sides of the equation.
\(\displaystyle -4x-19+19=21+19\)

Simplify.

\(\displaystyle -4x=40\) 

Divide both sides of the equation by \(\displaystyle -4\). 

\(\displaystyle \frac{-4x}{-4}=\frac{40}{-4}\)

Solve. When dividing a positive number with a negative number, our answer becomes negative.

\(\displaystyle x=-10\)

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle \frac{x}{4}-6=3\) 

Add \(\displaystyle 6\) to both sides of the equation.

\(\displaystyle \frac{x}{4}-6+6=3+6\)

Simplify.

\(\displaystyle \frac{x}{4}=9\) 

Multiply both sides of the eqaution by \(\displaystyle 4\).

\(\displaystyle (4)\frac{x}{4}=9(4)\)

Solve.

\(\displaystyle x=36\)

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle \frac{x}{11}-9=-18\) 

Add \(\displaystyle 9\) to both sides of the equation. 

\(\displaystyle \frac{x}{11}-9+9=-18+9\)

Remember since \(\displaystyle 18\) is greater than \(\displaystyle 9\) and is negative, our answer is negative. We will treat this operation as a subtraction problem.

\(\displaystyle \frac{x}{11}=-(18-9)\)

Simplify.

\(\displaystyle \frac{x}{11}=-9\) 

Multiply both sides of the equation by \(\displaystyle 11\).

\(\displaystyle (11)\frac{x}{11}=-9(11)\)

Solve. When multiplying a negative number by a positive number, our answer is negative.

\(\displaystyle x=-99\)

In order to solve for \(\displaystyle x\), we need to isolate it on the left side of the equation. We will do this by performing the same operations to both sides of the given equation:

\(\displaystyle \frac{x}{-3}-8=-17\) 

Add \(\displaystyle 8\) to both sides of the equation. 

\(\displaystyle \frac{x}{-3}-8+8=-17+8\)

Remember since \(\displaystyle 17\) is greater than \(\displaystyle 8\) and is negative, our answer is negative. We will treat this operation as a subtraction problem.

\(\displaystyle \frac{x}{-3}=-(17-8)\)

Simplify.

\(\displaystyle \frac{x}{-3}=-9\) 

Multiply both sides of the equation by \(\displaystyle -3\). 

\(\displaystyle (-3)\frac{x}{-3}=-9(-3)\)

Solve. When multiplying a negative number by a negative number, our answer is positive.

\(\displaystyle x=27\)

\(\displaystyle 6p + 4p + 3 = 7 (p - 2)\)

Combine like terms on the left and use distributive property on the right.

Use properties of equality to balance the equation.

\(\displaystyle 10p + 3 = 7p -14\)

\(\displaystyle -7p\)          \(\displaystyle -7p\)

\(\displaystyle 3p + 3 = -14\)

      \(\displaystyle - 3\)      \(\displaystyle - 3\)

\(\displaystyle 3p = -17\)

\(\displaystyle p = -\frac{17}{3}\)

Start by adding \(\displaystyle 5\) on both sides of the equation to yield:

\(\displaystyle 3x=18\). 

In order to get \(\displaystyle x\) by itself, we need to divide both sides of the equation by \(\displaystyle 3\). 

\(\displaystyle \frac{3x}{3}=\frac{18}{3}\).

This gives us

\(\displaystyle x=6\)

First, isolate variables and constants on either side of the equal sign. In this case, subtract \(\displaystyle 7\) from both sides. This gives us:

\(\displaystyle 4x=-36\).

Now divide both sides by \(\displaystyle 4\) to give us:

\(\displaystyle x=-9\).