Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+108} & = & \color{red}{135x} +20 \\\Leftrightarrow & 900x \color{red}{+108} \color{blue}{-108} \color{blue}{-135x} & = & \color{red}{135x} +20 \color{blue}{-135x} \color{blue}{-108} \\\Leftrightarrow & 900x-135x& = & 20-108 \\\Leftrightarrow & \color{red}{765} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{765} & & \\ & V = \left\{ \frac{-88}{765} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 15x-\frac{6}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{-54} & = & \color{red}{-315x} +50 \\\Leftrightarrow & 675x \color{red}{-54} \color{blue}{+54} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{+54} \\\Leftrightarrow & 675x+315x& = & 50+54 \\\Leftrightarrow & \color{red}{990} x& = & 104 \\\Leftrightarrow & x = \frac{104}{990} & & \\\Leftrightarrow & x = \frac{52}{495} & & \\ & V = \left\{ \frac{52}{495} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{231x} +22 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-30} \\\Leftrightarrow & -330x-231x& = & 22-30 \\\Leftrightarrow & \color{red}{-561} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-561} & & \\\Leftrightarrow & x = \frac{8}{561} & & \\ & V = \left\{ \frac{8}{561} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -2x+\frac{5}{8} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{+96} & = & \color{red}{-80x} +25 \\\Leftrightarrow & 600x \color{red}{+96} \color{blue}{-96} \color{blue}{+80x} & = & \color{red}{-80x} +25 \color{blue}{+80x} \color{blue}{-96} \\\Leftrightarrow & 600x+80x& = & 25-96 \\\Leftrightarrow & \color{red}{680} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{680} & & \\ & V = \left\{ \frac{-71}{680} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{18}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-54} & = & \color{red}{-105x} +40 \\\Leftrightarrow & 180x \color{red}{-54} \color{blue}{+54} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{+54} \\\Leftrightarrow & 180x+105x& = & 40+54 \\\Leftrightarrow & \color{red}{285} x& = & 94 \\\Leftrightarrow & x = \frac{94}{285} & & \\ & V = \left\{ \frac{94}{285} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & -4x+\frac{9}{4} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-16}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{+15} & = & \color{red}{-16x} +9 \\\Leftrightarrow & -60x \color{red}{+15} \color{blue}{-15} \color{blue}{+16x} & = & \color{red}{-16x} +9 \color{blue}{+16x} \color{blue}{-15} \\\Leftrightarrow & -60x+16x& = & 9-15 \\\Leftrightarrow & \color{red}{-44} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-44} & & \\\Leftrightarrow & x = \frac{3}{22} & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{18}{11}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1056}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1056x \color{red}{-144} & = & \color{red}{-440x} +77 \\\Leftrightarrow & 1056x \color{red}{-144} \color{blue}{+144} \color{blue}{+440x} & = & \color{red}{-440x} +77 \color{blue}{+440x} \color{blue}{+144} \\\Leftrightarrow & 1056x+440x& = & 77+144 \\\Leftrightarrow & \color{red}{1496} x& = & 221 \\\Leftrightarrow & x = \frac{221}{1496} & & \\\Leftrightarrow & x = \frac{13}{88} & & \\ & V = \left\{ \frac{13}{88} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & -9x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{8}{3}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{-81x} +4 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{+81x} & = & \color{red}{-81x} +4 \color{blue}{+81x} \color{blue}{-24} \\\Leftrightarrow & 90x+81x& = & 4-24 \\\Leftrightarrow & \color{red}{171} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{171} & & \\ & V = \left\{ \frac{-20}{171} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{792}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 792x \color{red}{-72} & = & \color{red}{220x} +99 \\\Leftrightarrow & 792x \color{red}{-72} \color{blue}{+72} \color{blue}{-220x} & = & \color{red}{220x} +99 \color{blue}{-220x} \color{blue}{+72} \\\Leftrightarrow & 792x-220x& = & 99+72 \\\Leftrightarrow & \color{red}{572} x& = & 171 \\\Leftrightarrow & x = \frac{171}{572} & & \\ & V = \left\{ \frac{171}{572} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{10}{7}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-10} & = & \color{red}{-63x} +10 \\\Leftrightarrow & 140x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & 140x+63x& = & 10+10 \\\Leftrightarrow & \color{red}{203} x& = & 20 \\\Leftrightarrow & x = \frac{20}{203} & & \\ & V = \left\{ \frac{20}{203} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 2x+\frac{7}{10} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 2x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{+140} & = & \color{red}{60x} +21 \\\Leftrightarrow & 1050x \color{red}{+140} \color{blue}{-140} \color{blue}{-60x} & = & \color{red}{60x} +21 \color{blue}{-60x} \color{blue}{-140} \\\Leftrightarrow & 1050x-60x& = & 21-140 \\\Leftrightarrow & \color{red}{990} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{990} & & \\ & V = \left\{ \frac{-119}{990} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{9})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 4x+\frac{4}{9}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{360}{ \color{blue}{90} }x+ \frac{40}{ \color{blue}{90} })& = & (\frac{630}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 360x \color{red}{+40} & = & \color{red}{630x} +81 \\\Leftrightarrow & 360x \color{red}{+40} \color{blue}{-40} \color{blue}{-630x} & = & \color{red}{630x} +81 \color{blue}{-630x} \color{blue}{-40} \\\Leftrightarrow & 360x-630x& = & 81-40 \\\Leftrightarrow & \color{red}{-270} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-270} & & \\\Leftrightarrow & x = \frac{-41}{270} & & \\ & V = \left\{ \frac{-41}{270} \right\} & \\\end{align}\)