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Consider the left side of the equation as



Match the right side of the equation to the indicated number of solutions.

Zero Solutions

One Solution

Infinite Solutions

Drag & Drop the answer
10x+1710x+1710x+17

10x+1810x+1810x+18

17x+1817x+1817x+18

7 answers

To determine how many solutions each equation has, we need to analyze the left and right sides.

  1. 10x + 17 = 10x + 17
  • This simplifies to \(0 = 0\), which means both sides are always equal for any value of \(x\).
  • Infinite Solutions
  1. 10x + 17 = 10x + 18
  • This simplifies to \(0 = 1\), which is a contradiction.
  • Zero Solutions
  1. 17x + 18 = 17x + 18
  • This simplifies also to \(0 = 0\), which is true for any \(x\).
  • Infinite Solutions

Now we can match them:

  • Zero Solutions: 10x + 17 = 10x + 18
  • One Solution: (No equation matches this category.)
  • Infinite Solutions: 10x + 17 = 10x + 17 and 17x + 18 = 17x + 18

So the final match result is:

  • Zero Solutions: 10x + 18
  • One Solution: (none)
  • Infinite Solutions: 10x + 17 and 17x + 18
Solve for the given variable.

8x+17=4x+58x+17=4x+58x+17=4x+5

x=x=x=

To solve for \( x \) in the equation \( 8x + 17 = 4x + 5 \), let's go through the steps:

  1. Start with the equation: \[ 8x + 17 = 4x + 5 \]

  2. Subtract \( 4x \) from both sides to get: \[ 8x - 4x + 17 = 5 \] This simplifies to: \[ 4x + 17 = 5 \]

  3. Next, subtract \( 17 \) from both sides: \[ 4x = 5 - 17 \] This simplifies to: \[ 4x = -12 \]

  4. Finally, divide both sides by \( 4 \): \[ x = -3 \]

So, \( x = -3 \).

If you have additional equations or variables to solve, please provide them, and I'll be happy to assist!

Solve the following linear equation.

−2y+4=20-2y+4=20−2y+4=20

y=y=y=

To solve the equation \(-2y + 4 = 20\), let's follow these steps:

  1. Start with the equation: \[ -2y + 4 = 20 \]

  2. Subtract \(4\) from both sides: \[ -2y = 20 - 4 \] This simplifies to: \[ -2y = 16 \]

  3. Now, divide both sides by \(-2\): \[ y = \frac{16}{-2} \] This gives: \[ y = -8 \]

So, the solution is \( y = -8 \).

Solve for the given variable.

−16z−17=−12z+5-16z-17=-12z+5−16z−17=−12z+5

z=z=z=

To solve the equation \( -16z - 17 = -12z + 5 \), let's follow these steps:

  1. Start with the given equation: \[ -16z - 17 = -12z + 5 \]

  2. First, add \( 16z \) to both sides to eliminate the \( -16z \) on the left: \[ -17 = 4z + 5 \]

  3. Next, subtract \( 5 \) from both sides: \[ -17 - 5 = 4z \] This simplifies to: \[ -22 = 4z \]

  4. Finally, divide both sides by \( 4 \): \[ z = \frac{-22}{4} \] Simplifying this, we get: \[ z = -\frac{11}{2} \quad \text{or} \quad z = -5.5 \]

So, the solution is: \[ z = -\frac{11}{2} \quad \text{or} \quad z = -5.5 \]