Question

3 more than the product of 7 and a number x is less than 26.
Write an inequality for the statement above.
Find the solution set for X.

Write the solution using a fraction or integer.

Answer 1

we know that

An inequality for the statement

$3$ more than the product of $7$ and a number x is less than $26$

is equal to

$3+7x < 26$

Find the solution set for X

$3+7x < 26 \\\\ 7x < 26-3\\\\ 7x < 23\\\\ x < \frac{23}{7} \\\\ x < 3\frac{2}{7}$

therefore

the answer is

the solution is the interval--------> (-∞,$3\frac{2}{7}$)

Answer 2

The solution of the inequality $3 + 7x < 26$ is $\boxed{x < \frac{{23}}{7}}{\text{  or  }}\boxed{x = 3\frac{2}{7}}.$

Further explanation:

The solutions of the linear inequality lie in the intervals.

If the linear equality is $x < a$, than the solutions of the inequality lies in the interval of $\boxed{\left( { - \infty ,a} \right)}.$

Given:

The statement is 3 more than the product of 7 and a number x is less than 26.

Explanation:

The inequality from the statement can be obtained as follows,

$3 + 7x < 26$

Solve the above inequality to obtained solution.

$\begin{aligned}3 + 7x &< 26\\3 + 7x - 3 &< 26 - 3\\7x &< 23\\\frac{{7x}}{7} &< \frac{{23}}{7}\\x &< \frac{{23}}{7}\\x&< 3\frac{2}{7}\\\end{aligned}$

The solution of the inequality $3 + 7x < 26$ is $\boxed{x < \frac{{23}}{7}}{\text{  or  }}\boxed{x = 3\frac{2}{7}}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequality

Keywords: inequality, statement, product, 3, more, number, less than, solution, solution set, fraction, integer, x.