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Inequalities are used to express unequal expressions.
The inequalities from the word problems are:
.
.
The statements from the inequalities are:
- -4 is not a solution to
- -6 is not a solution to
- -1 is not a solution to
- Graph b represents
<u>1. A number minus 3.5 is less than or equal to -2</u>
The statement can be broken down into the following expressions
So, when the expressions are brought together, we have:
<u>2. Zero is greater than or equal to twice a number x plus 1</u>
The statement can be broken down into the following expressions
So, when the expressions are brought together, we have:
<u />
<u>3. -1/2 is at least twice a number k minus 4</u>
The statement can be broken down into the following expressions
So, when the expressions are brought together, we have:
None of the options is correct
<h3>The solutions</h3><u>4. Tell whether -4 is a solution to x + 8 < -3</u>
We have:
Subtract 8 from both sides
The above inequality means that:
<em>x is less than -11</em>
-4 is not a solution, because -4 is greater than -11
<u>5. Tell whether -6 is a solution to 10 <= 3 - m</u>
We have:
Subtract 3 from both sides
Multiply both sides by -1 (the inequality sign changes)
Make m the subject
The above inequality means that:
<em>m is less than -7</em>
-6 is not a solution, because -6 is greater than -7
<u>6. Tell whether -1 is a solution to -3x <= -12.5</u>
We have:
Divide both sides by -3 (the inequality sign changes)
The above inequality means that:
<em>x is greater than or equal to </em><em />
-1 is not a solution, because -1 is less than <em />
The inequality is given as:
The less than sign (>) means that:
- The graph would use an open circle
- The arrow must point to the right
Only graph b satisfies this condition
Hence, the graph of is graph b
Read more about inequalities at: