Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{-12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -100x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -100x+35x& = & 6+12 \\\Leftrightarrow & \color{red}{-65} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-65} & & \\\Leftrightarrow & x = \frac{-18}{65} & & \\ & V = \left\{ \frac{-18}{65} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{9})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-56} & = & \color{red}{-441x} +54 \\\Leftrightarrow & 504x \color{red}{-56} \color{blue}{+56} \color{blue}{+441x} & = & \color{red}{-441x} +54 \color{blue}{+441x} \color{blue}{+56} \\\Leftrightarrow & 504x+441x& = & 54+56 \\\Leftrightarrow & \color{red}{945} x& = & 110 \\\Leftrightarrow & x = \frac{110}{945} & & \\\Leftrightarrow & x = \frac{22}{189} & & \\ & V = \left\{ \frac{22}{189} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -210x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & -210x+245x& = & 42-50 \\\Leftrightarrow & \color{red}{35} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & -3x+\frac{3}{11} \\\Leftrightarrow & 35x+\frac{21}{8}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{24}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{+231} & = & \color{red}{-264x} +24 \\\Leftrightarrow & 3080x \color{red}{+231} \color{blue}{-231} \color{blue}{+264x} & = & \color{red}{-264x} +24 \color{blue}{+264x} \color{blue}{-231} \\\Leftrightarrow & 3080x+264x& = & 24-231 \\\Leftrightarrow & \color{red}{3344} x& = & -207 \\\Leftrightarrow & x = \frac{-207}{3344} & & \\ & V = \left\{ \frac{-207}{3344} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{7})& = & -4x+\frac{9}{8} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -4x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1400}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1400x \color{red}{-160} & = & \color{red}{-224x} +63 \\\Leftrightarrow & 1400x \color{red}{-160} \color{blue}{+160} \color{blue}{+224x} & = & \color{red}{-224x} +63 \color{blue}{+224x} \color{blue}{+160} \\\Leftrightarrow & 1400x+224x& = & 63+160 \\\Leftrightarrow & \color{red}{1624} x& = & 223 \\\Leftrightarrow & x = \frac{223}{1624} & & \\ & V = \left\{ \frac{223}{1624} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{+270} & = & \color{red}{-441x} +28 \\\Leftrightarrow & -1890x \color{red}{+270} \color{blue}{-270} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{-270} \\\Leftrightarrow & -1890x+441x& = & 28-270 \\\Leftrightarrow & \color{red}{-1449} x& = & -242 \\\Leftrightarrow & x = \frac{-242}{-1449} & & \\\Leftrightarrow & x = \frac{242}{1449} & & \\ & V = \left\{ \frac{242}{1449} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{9})& = & 5x+\frac{7}{10} \\\Leftrightarrow & 12x-\frac{20}{9}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1080}{ \color{blue}{90} }x- \frac{200}{ \color{blue}{90} })& = & (\frac{450}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1080x \color{red}{-200} & = & \color{red}{450x} +63 \\\Leftrightarrow & 1080x \color{red}{-200} \color{blue}{+200} \color{blue}{-450x} & = & \color{red}{450x} +63 \color{blue}{-450x} \color{blue}{+200} \\\Leftrightarrow & 1080x-450x& = & 63+200 \\\Leftrightarrow & \color{red}{630} x& = & 263 \\\Leftrightarrow & x = \frac{263}{630} & & \\ & V = \left\{ \frac{263}{630} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{5})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 14x+\frac{14}{5}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{630}{ \color{blue}{45} }x+ \frac{126}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 630x \color{red}{+126} & = & \color{red}{225x} +50 \\\Leftrightarrow & 630x \color{red}{+126} \color{blue}{-126} \color{blue}{-225x} & = & \color{red}{225x} +50 \color{blue}{-225x} \color{blue}{-126} \\\Leftrightarrow & 630x-225x& = & 50-126 \\\Leftrightarrow & \color{red}{405} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{405} & & \\ & V = \left\{ \frac{-76}{405} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{7})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 10x+\frac{20}{7}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+220} & = & \color{red}{-231x} +70 \\\Leftrightarrow & 770x \color{red}{+220} \color{blue}{-220} \color{blue}{+231x} & = & \color{red}{-231x} +70 \color{blue}{+231x} \color{blue}{-220} \\\Leftrightarrow & 770x+231x& = & 70-220 \\\Leftrightarrow & \color{red}{1001} x& = & -150 \\\Leftrightarrow & x = \frac{-150}{1001} & & \\ & V = \left\{ \frac{-150}{1001} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{75x} +40 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 270x-75x& = & 40-36 \\\Leftrightarrow & \color{red}{195} x& = & 4 \\\Leftrightarrow & x = \frac{4}{195} & & \\ & V = \left\{ \frac{4}{195} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-40} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 440x \color{red}{-40} \color{blue}{+40} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+40} \\\Leftrightarrow & 440x+308x& = & 99+40 \\\Leftrightarrow & \color{red}{748} x& = & 139 \\\Leftrightarrow & x = \frac{139}{748} & & \\ & V = \left\{ \frac{139}{748} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+30} & = & \color{red}{-245x} +14 \\\Leftrightarrow & -350x \color{red}{+30} \color{blue}{-30} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{-30} \\\Leftrightarrow & -350x+245x& = & 14-30 \\\Leftrightarrow & \color{red}{-105} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-105} & & \\\Leftrightarrow & x = \frac{16}{105} & & \\ & V = \left\{ \frac{16}{105} \right\} & \\\end{align}\)