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Chapter 6: Problem 25

Solve each inequality and graph the solution set on a number line. \(3 x+3<18\)

Short Answer

Expert verified
The solution set is \(x < 5\). On the number line, all numbers less than 5 are included in the solution set, any position less than 5 is marked with an open circle.

Step by step solution

01

Simplify the inequality

Firstly, attempt to simplify the inequality by subtracting 3 from both sides. Doing this, you have \(3x < 18 - 3\), simplifying it further gives \(3x < 15\)
02

Isolate x

Next, to isolate 'x', divide every term by 3. So, \(x < \frac{15}{3}\). It simplifies to \(x < 5\)
03

Draw the number line

Draw a line, representing numbers. Create markers for values less than 5. Since x is strictly less than 5 (not equal to 5), draw an open circle at 5

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Most popular questions from this chapter

Solve the equations using the quadratic formula. \(x^{2}-2 x-10=0\)

Solve each equation by the method of your choice. \(2 x^{2}-9 x-3=9-9 x\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. In an inequality such as \(5 x+4<8 x-5\), I can avoid division by a negative number depending on which side I collect the variable terms and on which side I collect the constant terms.

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-8 x+32\)

Use FOIL to find the products. \((x-1)(x+2)\)
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