Maths-
General
Easy

Question

How is the solution to -4(2x-3)>36 similar to and different from the solution-4(2x-3)=36 .

hintHint:

An equation is a mathematical statement that equates two equal expressions. Linear inequalities are expressions where any two values are compared by the inequality symbols<,>,≤&≥ .
We are asked to find the similarities and differences between the given inequality and the equation.

The correct answer is: -3=x


    Step 1 of 2:
    The solution of the inequality, -4(2x-3)>36 is:
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative 4 left parenthesis 2 x minus 3 right parenthesis greater than 36 end cell row cell negative 8 x plus 12 greater than 36 end cell row cell negative 36 plus 12 greater than 8 x end cell row cell negative 24 greater than 8 x end cell row cell fraction numerator negative 24 over denominator 8 end fraction greater than x end cell row cell negative 3 greater than x end cell end table

    This means that the variable x takes all real values less than -3. That is, numbers less than -3 are solutions of the inequality.
    Step 2 of 2:
    The solution of the equation -4(2x-3)=36 is:
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative 4 left parenthesis 2 x minus 3 right parenthesis equals 36 end cell row cell negative 8 x plus 12 equals 36 end cell row cell 12 minus 36 equals 8 x end cell row cell negative 24 equals 8 x end cell row cell fraction numerator negative 24 over denominator 8 end fraction equals x end cell row cell negative 3 equals x end cell end table
    Here, the solution of the equation is .

    The number of solutions for an inequality can be infinity. Whereas, a linear equation has only a maximum of one solution.

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