We read your photo as:

To determine the value of t in the given equation, we will first find a common denominator to clear the fractions.

Mathematics

ScanSolve AI Answer

Answer

-15

Step-by-step solution

5 steps

To determine the value of tt in the given equation, we will first find a common denominator to clear the fractions.

The equation is:

17+2t3=15t−321+1\frac{1}{7} + \frac{2t}{3} = \frac{15t - 3}{21} + 1

  1. Find the least common multiple (LCM) of the denominators 7, 3, and 21.

    The LCM of 7, 3, and 21 is 21.

  2. Multiply every term in the equation by the LCM (21) to eliminate the denominators.

    21(17)+21(2t3)=21(15t−321)+21(1)21 \left( \frac{1}{7} \right) + 21 \left( \frac{2t}{3} \right) = 21 \left( \frac{15t - 3}{21} \right) + 21 (1)

  3. Simplify each term.

    217+42t3=(15t−3)+21\frac{21}{7} + \frac{42t}{3} = (15t - 3) + 21 3+14t=15t−3+213 + 14t = 15t - 3 + 21

  4. Combine the constant terms on the right side of the equation.

    3+14t=15t+183 + 14t = 15t + 18

  5. Isolate the terms with tt on one side and the constant terms on the other side.

    Subtract 14t14t from both sides:

    3=15t−14t+183 = 15t - 14t + 18 3=t+183 = t + 18

    Subtract 18 from both sides:

    3−18=t3 - 18 = t −15=t-15 = t

    The value of tt is:

    −15-15
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QFind a common denominator for the two fractions.QCalculate the value of t.QSolve the equation (4t)/(9) − 5 = 3 for t and identify the correct option.QSolve the equation: 3/(t−2) = 4/(3t+4)QTo simplify the expression, we will first simplify the numerator and the denominator separately…
Browse by topic:Pre-Algebra
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp