Intermediate Algebra
Solve the following linear equation for xx: 12x+7=19\(\displaystyle\]\frac\)12x+7=19
If a linear equation simplifies to the statement 0=00 = 0 after correctly combining like terms, what conclusion can be drawn about the original equation?
A pharmacist combines 38x\(\displaystyle\) \(\frac{3}{8}\)x liters of Solution A with 14x\(\displaystyle\) \(\frac{1}{4}\)x liters of Solution B to create a 22-liter mixture. By clearing the fractions first, determine the value of the scale factor xx.
Solve the inequality x4<3\(\displaystyle\]\frac{x}{4}\)<3.
Which of the following best describes the fundamental difference between the solution to a linear equation (e.g., ax+b=cax + b = c) and a linear inequality (e.g., ax+b>cax + b > c)?
Solve the inequality 2(x+4)−32x<5+x4\(\displaystyle\) 2(x + 4) - \(\frac{3}{2}\)x < 5 + \(\frac{x}{4}\) for xx.
A number line shows an open circle at x=3x = 3 and shading to the right. Which inequality best matches this graph?
Solve −34x≤9-\(\frac\)34x\(\le\)9 and express the answer in inequality form and interval notation.
Let A={a,b,c}A={\(\left\[\lbrace\) a,b,c\(\right\]\rbrace\)}, B={b,c,d}B={\(\left\[\lbrace\) b,c,d\(\right\]\rbrace\)}, and C={c,e}C={\(\left\[\lbrace\) c,e\(\right\]\rbrace\)}. Compute A∩(B∪C)A ∩ (B ∪ C).
Why does the equation ∣x∣=−3|x| = -3 have no real solutions?
Solve ∣3x−9∣=0|3x - 9| = 0.
Solve ∣2x−1∣=∣x+5∣|2x - 1| = |x + 5|.
