Question

How many solutions does this equation have?

–4s = –10 − 5s
does it have 1 solution or zero or infinity many solutions

Answer 1

Explanation

• Solve the equation for s-term.

$- 4s = - 10 - 5s \\ - 4s + 5s = - 10 \\ s = - 10$

• Answer Check by substituting s = -10 in the equation.

$- 4( - 10) = - 10 - 5( - 10) \\ 40 = - 10 + 50 \\ 40 = 40 \: \: \tiny \boxed{ \green \checkmark}$

• Solutions

No Solutions

When both sides of equation are different. For example, 3 = 4 which makes the equation false. That means the equation is false for all real numbers, thus having no solutions.

One Solution

A common type solution because you see this type of solution a lot. If you can solve the equation for a variable like x = 2 or s = 0. That's one solution.

Infinitely Many Solutions

When both sides are same like 3 = 3 or 7 = 7. That means the equation is true for all real numbers. You can see this type of solution by solving the equation with same both sides like 3x+2 = 3x+2.

Answer

• Because we can solve the equation for s-term. Therefore the answer is one solution