Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

  1. \(3(-5x-\frac{2}{5})=-8x+\frac{4}{3}\)
  2. \(-7(-4x+\frac{3}{11})=9x+\frac{9}{8}\)
  3. \(5(2x+\frac{5}{6})=-7x+\frac{7}{8}\)
  4. \(7(5x-\frac{2}{5})=8x+\frac{10}{3}\)
  5. \(5(4x-\frac{3}{11})=-3x+\frac{9}{4}\)
  6. \(2(-3x+\frac{4}{9})=7x+\frac{4}{11}\)
  7. \(-3(2x+\frac{2}{7})=-7x+\frac{6}{5}\)
  8. \(-5(2x+\frac{4}{9})=-7x+\frac{6}{11}\)
  9. \(7(4x+\frac{4}{3})=9x+\frac{2}{7}\)
  10. \(2(2x+\frac{3}{5})=5x+\frac{9}{10}\)
  11. \(-3(-5x+\frac{2}{7})=8x+\frac{3}{2}\)
  12. \(-4(-2x-\frac{5}{7})=-5x+\frac{10}{7}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -15x-\frac{6}{5}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-18} & = & \color{red}{-120x} +20 \\\Leftrightarrow & -225x \color{red}{-18} \color{blue}{+18} \color{blue}{+120x} & = & \color{red}{-120x} +20 \color{blue}{+120x} \color{blue}{+18} \\\Leftrightarrow & -225x+120x& = & 20+18 \\\Leftrightarrow & \color{red}{-105} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-105} & & \\\Leftrightarrow & x = \frac{-38}{105} & & \\ & V = \left\{ \frac{-38}{105} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{11})& = & 9x+\frac{9}{8} \\\Leftrightarrow & 28x-\frac{21}{11}& = & 9x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x- \frac{168}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{-168} & = & \color{red}{792x} +99 \\\Leftrightarrow & 2464x \color{red}{-168} \color{blue}{+168} \color{blue}{-792x} & = & \color{red}{792x} +99 \color{blue}{-792x} \color{blue}{+168} \\\Leftrightarrow & 2464x-792x& = & 99+168 \\\Leftrightarrow & \color{red}{1672} x& = & 267 \\\Leftrightarrow & x = \frac{267}{1672} & & \\ & V = \left\{ \frac{267}{1672} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{6})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 10x+\frac{25}{6}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 6 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x+ \frac{100}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{+100} & = & \color{red}{-168x} +21 \\\Leftrightarrow & 240x \color{red}{+100} \color{blue}{-100} \color{blue}{+168x} & = & \color{red}{-168x} +21 \color{blue}{+168x} \color{blue}{-100} \\\Leftrightarrow & 240x+168x& = & 21-100 \\\Leftrightarrow & \color{red}{408} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{408} & & \\ & V = \left\{ \frac{-79}{408} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{5})& = & 8x+\frac{10}{3} \\\Leftrightarrow & 35x-\frac{14}{5}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x- \frac{42}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{-42} & = & \color{red}{120x} +50 \\\Leftrightarrow & 525x \color{red}{-42} \color{blue}{+42} \color{blue}{-120x} & = & \color{red}{120x} +50 \color{blue}{-120x} \color{blue}{+42} \\\Leftrightarrow & 525x-120x& = & 50+42 \\\Leftrightarrow & \color{red}{405} x& = & 92 \\\Leftrightarrow & x = \frac{92}{405} & & \\ & V = \left\{ \frac{92}{405} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{11})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 20x-\frac{15}{11}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{880}{ \color{blue}{44} }x- \frac{60}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 880x \color{red}{-60} & = & \color{red}{-132x} +99 \\\Leftrightarrow & 880x \color{red}{-60} \color{blue}{+60} \color{blue}{+132x} & = & \color{red}{-132x} +99 \color{blue}{+132x} \color{blue}{+60} \\\Leftrightarrow & 880x+132x& = & 99+60 \\\Leftrightarrow & \color{red}{1012} x& = & 159 \\\Leftrightarrow & x = \frac{159}{1012} & & \\ & V = \left\{ \frac{159}{1012} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{9})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{+88} & = & \color{red}{693x} +36 \\\Leftrightarrow & -594x \color{red}{+88} \color{blue}{-88} \color{blue}{-693x} & = & \color{red}{693x} +36 \color{blue}{-693x} \color{blue}{-88} \\\Leftrightarrow & -594x-693x& = & 36-88 \\\Leftrightarrow & \color{red}{-1287} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-1287} & & \\\Leftrightarrow & x = \frac{4}{99} & & \\ & V = \left\{ \frac{4}{99} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & -210x+245x& = & 42+30 \\\Leftrightarrow & \color{red}{35} x& = & 72 \\\Leftrightarrow & x = \frac{72}{35} & & \\ & V = \left\{ \frac{72}{35} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{9})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{20}{9}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-220} & = & \color{red}{-693x} +54 \\\Leftrightarrow & -990x \color{red}{-220} \color{blue}{+220} \color{blue}{+693x} & = & \color{red}{-693x} +54 \color{blue}{+693x} \color{blue}{+220} \\\Leftrightarrow & -990x+693x& = & 54+220 \\\Leftrightarrow & \color{red}{-297} x& = & 274 \\\Leftrightarrow & x = \frac{274}{-297} & & \\\Leftrightarrow & x = \frac{-274}{297} & & \\ & V = \left\{ \frac{-274}{297} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & 9x+\frac{2}{7} \\\Leftrightarrow & 28x+\frac{28}{3}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{+196} & = & \color{red}{189x} +6 \\\Leftrightarrow & 588x \color{red}{+196} \color{blue}{-196} \color{blue}{-189x} & = & \color{red}{189x} +6 \color{blue}{-189x} \color{blue}{-196} \\\Leftrightarrow & 588x-189x& = & 6-196 \\\Leftrightarrow & \color{red}{399} x& = & -190 \\\Leftrightarrow & x = \frac{-190}{399} & & \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 4x+\frac{6}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{+12} & = & \color{red}{50x} +9 \\\Leftrightarrow & 40x \color{red}{+12} \color{blue}{-12} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{-12} \\\Leftrightarrow & 40x-50x& = & 9-12 \\\Leftrightarrow & \color{red}{-10} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-10} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 8x+\frac{3}{2} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 8x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-12} & = & \color{red}{112x} +21 \\\Leftrightarrow & 210x \color{red}{-12} \color{blue}{+12} \color{blue}{-112x} & = & \color{red}{112x} +21 \color{blue}{-112x} \color{blue}{+12} \\\Leftrightarrow & 210x-112x& = & 21+12 \\\Leftrightarrow & \color{red}{98} x& = & 33 \\\Leftrightarrow & x = \frac{33}{98} & & \\ & V = \left\{ \frac{33}{98} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{20}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+20} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 56x \color{red}{+20} \color{blue}{-20} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{-20} \\\Leftrightarrow & 56x+35x& = & 10-20 \\\Leftrightarrow & \color{red}{91} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{91} & & \\ & V = \left\{ \frac{-10}{91} \right\} & \\\end{align}\)
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