Solve. The symbol indicates an exercise designed to give practice using a calculator. -(x)/(7)=(

step 1 solve the equation negative x over 7 is equal to 2 9th. And the way that you're going to do that

Solve. The symbol indicates an exercise designed to give...

Key Concepts

Linear Equations

A linear equation is an algebraic statement where the highest power of the variable is one. This type of equation represents a straight line when graphed and typically involves finding a single solution by performing operations that simplify the equation to isolate the unknown variable.

Equations Involving Fractions

Equations that include fractions require careful manipulation of numerators and denominators. The process often involves eliminating fractions by multiplying both sides of the equation by the common denominator or directly using the multiplicative inverse to simplify the expression and isolate the variable.

Multiplicative Inverse

The multiplicative inverse, or reciprocal, of a number is used to cancel out coefficients when isolating a variable. In equations involving fractions, multiplying by the reciprocal of the coefficient effectively 'undoes' the multiplication and helps in solving for the variable.

Transcript

00:01 Solve the equation negative x over 7 is equal to 2 9th.

00:04 And the way that you're going to do that is you're going to want to get rid of that divide by negative 7 that's on the left down side because you want to get the value of 1x.

00:12 So an easy way to think about this is think of this as negative 1 7x is equal to 9th.

00:22 And then you can undo the times by negative 1 7th by multiplying both sides by the reciprocal of negative 1 7th, which is of course negative.

00:32 7 over 1.

00:34 So if you multiply both sides of the equation by negative 7, you're going to cancel out the negative 1 -7th because the negative times the negative is a positive.

00:42 And that's going to be 7th, which is 1.

00:45 So you're going to get positive 1x is equal to.

00:47 On the other side, you're going to get negative 7 times positive 2 .9th.

00:52 Negative times a positive is a negative value.

00:55 And 7 times 2 is 14.

00:56 So that'll be negative 14 .9th, which is the answer.

01:01 You could simplify that.

01:02 To a mixed number if you wanted to.

01:04 Nine goes into 14 how many times, once, with how many left over, five.

01:09 So you can think of it as 1 in 5 ninth, negative 1 in 5 nights, i should say.

01:14 Which is the same as negative 1 .5 repeating, okay? so all of these are versions of the answer that are correct.

01:21 I personally like this one as a way of checking my answer.