The solution to the inequality [tex]3x-3\leq -15\,\,or\,\,4x-1\geq 11[/tex] is [tex]x\leq -3\,\,or\,\,x\geq 4[/tex]
The number line is shown in figure attached.
Step-by-step explanation:
We need to solve the inequality: [tex]3x-3\leq -15\,\,or\,\,4x-1\geq 11[/tex]
Solving the inequality:
[tex]3x-3\leq -15\,\,or\,\,4x-1\geq 11\\Adding\,\,3\,\,on\,\,both\,\,sides\,\,and\,\,1\,\,on\,\,both\,\,sides\\3x-3+3\leq -15+3\,\,or\,\,4x-1+1\geq 11+1\\3x\leq -12\,\,or\,\,4x\geq 12[/tex]
Divide by 3 and divide by 12
[tex]x\leq \frac{-12}{3} \,\,or\,\,x\geq \frac{12}{4} \\x\leq -4\,\,or\,\,x\geq 3[/tex]
So, value of x can be less than equal to -4 or value of x is greater than equal to 3.
The number line is shown in figure attached.
The solution to the inequality [tex]3x-3\leq -15\,\,or\,\,4x-1\geq 11[/tex] is [tex]x\leq -3\,\,or\,\,x\geq 4[/tex]
Keywords: Solving inequalities
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