Solve the following algebraic equations and inequalities: 1. 2x + 3 = 4x 2. 2a + 3 = 7x − 6 3. 6x − 5

Question

Solve the following algebraic equations and inequalities: 1. 2x + 3 = 4x 2. 2a + 3 = 7x − 6 3. 6x − 5 < 8x 4. (3x+5)/2 >= (6x+1)/2

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems, with detailed steps:

:

2x + 3 = 4x

Subtract $2x$ from both sides of the equation to gather $x$ terms on one side.
$3 = 4x - 2x$
Combine the $x$ terms.
$3 = 2x$
Divide both sides by 2 to solve for $x$ .
$\frac{3}{2} = \frac{2x}{2}$ $x = \frac{3}{2}$
Your solution for this problem is correct.
$\boxed{x = \frac{3}{2}}$
:
$2a + 3 = 7x - 6$
Add 6 to both sides of the equation to isolate the term containing $x$ .
$2a + 3 + 6 = 7x$ $2a + 9 = 7x$
Divide both sides by 7 to solve for $x$ .
$\frac{2a + 9}{7} = \frac{7x}{7}$ $x = \frac{2a + 9}{7}$ $\boxed{x = \frac{2a + 9}{7}}$
:
$6x - 5 < 8x$
Subtract $8x$ from both sides of the inequality to gather $x$ terms on the left.
$6x - 8x - 5 < 0$ $-2x - 5 < 0$
Add 5 to both sides to move the constant term to the right.
$-2x < 5$
Divide both sides by $-2$ .
When dividing an inequality by a negative number, you must flip the direction of the inequality sign.
$\frac{-2x}{-2} > \frac{5}{-2}$ $x > -\frac{5}{2}$ $\boxed{x > -\frac{5}{2}}$
:
$\frac{3x+5}{2} \ge \frac{6x+1}{2}$
Multiply both sides of the inequality by 2 to eliminate the denominators.
$2 \times \left(\frac{3x+5}{2}\right) \ge 2 \times \left(\frac{6x+1}{2}\right)$ $3x+5 \ge 6x+1$
Subtract $6x$ from both sides to gather $x$ terms on the left.
$3x - 6x + 5 \ge 1$ $-3x + 5 \ge 1$
Subtract 5 from both sides to move the constant term to the right.
$-3x \ge 1 - 5$ $-3x \ge -4$
Divide both sides by $-3$ .
Remember to flip the inequality sign because you are dividing by a negative number.
$\frac{-3x}{-3} \le \frac{-4}{-3}$ $x \le \frac{4}{3}$ $\boxed{x \le \frac{4}{3}}$

Solve the following algebraic equations and inequalities: 1. 2x + 3 = 4x 2. 2a + 3 = 7x − 6 3. 6x − 5 < 8x 4. (3x+5)/2 >= (6x+1)/2

Step-by-step solution

Subtract $2x$ from both sides of the equation to gather $x$ terms on one side.

Combine the $x$ terms.

Divide both sides by 2 to solve for $x$ .

Add 6 to both sides of the equation to isolate the term containing $x$ .

Divide both sides by 7 to solve for $x$ .

Subtract $8x$ from both sides of the inequality to gather $x$ terms on the left.

Add 5 to both sides to move the constant term to the right.

Divide both sides by $-2$ .

Multiply both sides of the inequality by 2 to eliminate the denominators.

Subtract $6x$ from both sides to gather $x$ terms on the left.

Subtract 5 from both sides to move the constant term to the right.

Divide both sides by $-3$ .

Still stuck on this one?

More Mathematics Questions

Solve the following algebraic equations and inequalities: 1. 2x + 3 = 4x 2. 2a + 3 = 7x − 6 3. 6x − 5 < 8x 4. (3x+5)/2 >= (6x+1)/2

Step-by-step solution

Subtract 2x2x2x from both sides of the equation to gather xxx terms on one side.

Combine the xxx terms.

Divide both sides by 2 to solve for xxx.

Add 6 to both sides of the equation to isolate the term containing xxx.

Divide both sides by 7 to solve for xxx.

Subtract 8x8x8x from both sides of the inequality to gather xxx terms on the left.

Add 5 to both sides to move the constant term to the right.

Divide both sides by −2-2−2.

Multiply both sides of the inequality by 2 to eliminate the denominators.

Subtract 6x6x6x from both sides to gather xxx terms on the left.

Subtract 5 from both sides to move the constant term to the right.

Divide both sides by −3-3−3.

Still stuck on this one?

More Mathematics Questions

Subtract $2x$ from both sides of the equation to gather $x$ terms on one side.

Combine the $x$ terms.

Divide both sides by 2 to solve for $x$ .

Add 6 to both sides of the equation to isolate the term containing $x$ .

Divide both sides by 7 to solve for $x$ .

Subtract $8x$ from both sides of the inequality to gather $x$ terms on the left.

Divide both sides by $-2$ .

Subtract $6x$ from both sides to gather $x$ terms on the left.

Divide both sides by $-3$ .