Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for zz.\newline7=∣z+2∣7 = |z + 2|\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinez=z = _____ or z=z = _____

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve absolute value equationsright chevron icon

Full solution

Q. Solve for zz.\newline7=∣z+2∣7 = |z + 2|\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinez=z = _____ or z=z = _____
  1. Understand absolute value equation: Understand the absolute value equation.\newlineThe equation 7=∣z+2∣7 = |z + 2| means that the expression inside the absolute value, z+2z + 2, can either be 77 or −7-7, because the absolute value of a number is always non-negative.
  2. Set up two equations: Set up two separate equations to solve for zz. Since ∣z+2∣|z + 2| can be 77 or −7-7, we have two cases: Case 11: z+2=7z + 2 = 7 Case 22: z+2=−7z + 2 = -7
  3. Solve for z in Case 11: Solve for z in Case 11.\newlineStarting with z+2=7z + 2 = 7, subtract 22 from both sides to isolate zz.\newlinez+2−2=7−2z + 2 - 2 = 7 - 2\newlinez=5z = 5
  4. Solve for zz in Case 22: Solve for zz in Case 22.\newlineStarting with z+2=−7z + 2 = -7, subtract 22 from both sides to isolate zz.\newlinez+2−2=−7−2z + 2 - 2 = -7 - 2\newlinez=−9z = -9

More problems from Solve absolute value equations

Question
Solve for zz.\newline7=7∣z∣7 = 7|z|\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinez=z = _____ or z=z = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for ww.\newline0=−3∣w∣0 = -3|w|\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinew=w = _____ or w=w = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for jj.\newline∣j+6∣=0|j + 6| = 0\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinej=j = _____ or j=j = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for uu.\newline∣u−3∣=3|u - 3| = 3\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineu=u = _____ or u=u = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for yy.\newline−8=∣y∣−8-8 = |y| - 8\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newliney=y = _____ or y=y = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for ff.\newline∣−3f∣=3|-3f| = 3\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinef=f = _____ or f=f = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for vv.\newline−6∣v∣=−6-6|v| = -6\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinev=v = _____ or v=v = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for gg.\newline∣−3g∣=0|-3g| = 0\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineg=g = _____ or g=g = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for uu.\newline−3=∣u∣−7-3 = |u| - 7\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineu=u = _____ or u=u = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for qq.\newline∣q∣−6=−5|q| - 6 = -5\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineq=q = _____ or q=q = _____
Get tutor helpright-arrow

Posted 8 months ago

View all (21)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant