Solved on Feb 22, 2024

Solve the inequality $2(3x-1)<2$ for real values of $x$ .

STEP 1

Assumptions
1. We are given the inequality $2(3x - 1) < 2$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to distribute the 2 across the terms inside the parentheses.
$2(3x) - 2(1) < 2$

STEP 3

Perform the multiplication.
$6x - 2 < 2$

STEP 4

Next, we need to isolate the term containing $x$ on one side of the inequality. We can do this by adding 2 to both sides of the inequality.
$6x - 2 + 2 < 2 + 2$

STEP 5

Simplify both sides of the inequality.
$6x < 4$

STEP 6

Now, to solve for $x$ , we need to divide both sides of the inequality by 6.
$\frac{6x}{6} < \frac{4}{6}$

STEP 7

Simplify the fractions.
$x < \frac{2}{3}$
The solution to the inequality is $x < \frac{2}{3}$ .

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Solve the inequality $2(3x-1)<2$ for real values of $x$ .

STEP 1

Assumptions
1. We are given the inequality $2(3x - 1) < 2$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to distribute the 2 across the terms inside the parentheses.
$2(3x) - 2(1) < 2$

STEP 3

Perform the multiplication.
$6x - 2 < 2$

STEP 4

Next, we need to isolate the term containing $x$ on one side of the inequality. We can do this by adding 2 to both sides of the inequality.
$6x - 2 + 2 < 2 + 2$

STEP 5

Simplify both sides of the inequality.
$6x < 4$

STEP 6

Now, to solve for $x$ , we need to divide both sides of the inequality by 6.
$\frac{6x}{6} < \frac{4}{6}$

STEP 7

Simplify the fractions.
$x < \frac{2}{3}$
The solution to the inequality is $x < \frac{2}{3}$ .

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Solve the inequality 2(3x−1)<22(3x-1)<22(3x−1)<2 for real values of xxx.

STEP 1

Assumptions1. We are given the inequality 2(3x−1)<22(3x - 1) < 22(3x−1)<2.2. We need to solve for the variable xxx.

STEP 2

First, we need to distribute the 2 across the terms inside the parentheses.2(3x)−2(1)<22(3x) - 2(1) < 22(3x)−2(1)<2

STEP 3

Perform the multiplication.6x−2<26x - 2 < 26x−2<2

STEP 4

Next, we need to isolate the term containing xxx on one side of the inequality. We can do this by adding 2 to both sides of the inequality.6x−2+2<2+26x - 2 + 2 < 2 + 26x−2+2<2+2

STEP 5

Simplify both sides of the inequality.6x<46x < 46x<4

STEP 6

Now, to solve for xxx, we need to divide both sides of the inequality by 6.6x6<46\frac{6x}{6} < \frac{4}{6}66x​<64​

STEP 7

Simplify the fractions.x<23x < \frac{2}{3}x<32​The solution to the inequality is x<23x < \frac{2}{3}x<32​.

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Solve the inequality $2(3x-1)<2$ for real values of $x$ .

Assumptions
1. We are given the inequality $2(3x - 1) < 2$ .
2. We need to solve for the variable $x$ .

First, we need to distribute the 2 across the terms inside the parentheses.
$2(3x) - 2(1) < 2$

Perform the multiplication.
$6x - 2 < 2$

Next, we need to isolate the term containing $x$ on one side of the inequality. We can do this by adding 2 to both sides of the inequality.
$6x - 2 + 2 < 2 + 2$

Simplify both sides of the inequality.
$6x < 4$

Now, to solve for $x$ , we need to divide both sides of the inequality by 6.
$\frac{6x}{6} < \frac{4}{6}$

Simplify the fractions.
$x < \frac{2}{3}$
The solution to the inequality is $x < \frac{2}{3}$ .