Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{9})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 4x+\frac{8}{9}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{-81x} +10 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{-8} \\\Leftrightarrow & 36x+81x& = & 10-8 \\\Leftrightarrow & \color{red}{117} x& = & 2 \\\Leftrightarrow & x = \frac{2}{117} & & \\ & V = \left\{ \frac{2}{117} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{3})& = & -8x+\frac{7}{10} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{+140} & = & \color{red}{-240x} +21 \\\Leftrightarrow & -630x \color{red}{+140} \color{blue}{-140} \color{blue}{+240x} & = & \color{red}{-240x} +21 \color{blue}{+240x} \color{blue}{-140} \\\Leftrightarrow & -630x+240x& = & 21-140 \\\Leftrightarrow & \color{red}{-390} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-390} & & \\\Leftrightarrow & x = \frac{119}{390} & & \\ & V = \left\{ \frac{119}{390} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{3})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 28x-\frac{28}{3}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x- \frac{224}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{-224} & = & \color{red}{-216x} +21 \\\Leftrightarrow & 672x \color{red}{-224} \color{blue}{+224} \color{blue}{+216x} & = & \color{red}{-216x} +21 \color{blue}{+216x} \color{blue}{+224} \\\Leftrightarrow & 672x+216x& = & 21+224 \\\Leftrightarrow & \color{red}{888} x& = & 245 \\\Leftrightarrow & x = \frac{245}{888} & & \\ & V = \left\{ \frac{245}{888} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{11})& = & -2x+\frac{4}{9} \\\Leftrightarrow & 35x+\frac{14}{11}& = & -2x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x+ \frac{126}{ \color{blue}{99} })& = & (\frac{-198}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{+126} & = & \color{red}{-198x} +44 \\\Leftrightarrow & 3465x \color{red}{+126} \color{blue}{-126} \color{blue}{+198x} & = & \color{red}{-198x} +44 \color{blue}{+198x} \color{blue}{-126} \\\Leftrightarrow & 3465x+198x& = & 44-126 \\\Leftrightarrow & \color{red}{3663} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{3663} & & \\ & V = \left\{ \frac{-82}{3663} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+32} & = & \color{red}{-140x} +63 \\\Leftrightarrow & 336x \color{red}{+32} \color{blue}{-32} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{-32} \\\Leftrightarrow & 336x+140x& = & 63-32 \\\Leftrightarrow & \color{red}{476} x& = & 31 \\\Leftrightarrow & x = \frac{31}{476} & & \\ & V = \left\{ \frac{31}{476} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & -8x+\frac{9}{4} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -8x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-224}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{-40} & = & \color{red}{-224x} +63 \\\Leftrightarrow & -420x \color{red}{-40} \color{blue}{+40} \color{blue}{+224x} & = & \color{red}{-224x} +63 \color{blue}{+224x} \color{blue}{+40} \\\Leftrightarrow & -420x+224x& = & 63+40 \\\Leftrightarrow & \color{red}{-196} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-196} & & \\\Leftrightarrow & x = \frac{-103}{196} & & \\ & V = \left\{ \frac{-103}{196} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 420x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{595} x& = & 99 \\\Leftrightarrow & x = \frac{99}{595} & & \\ & V = \left\{ \frac{99}{595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{7})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+100} & = & \color{red}{315x} +56 \\\Leftrightarrow & 700x \color{red}{+100} \color{blue}{-100} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{-100} \\\Leftrightarrow & 700x-315x& = & 56-100 \\\Leftrightarrow & \color{red}{385} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{385} & & \\\Leftrightarrow & x = \frac{-4}{35} & & \\ & V = \left\{ \frac{-4}{35} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{5})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -10x-\frac{8}{5}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{72}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-72} & = & \color{red}{-315x} +40 \\\Leftrightarrow & -450x \color{red}{-72} \color{blue}{+72} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{+72} \\\Leftrightarrow & -450x+315x& = & 40+72 \\\Leftrightarrow & \color{red}{-135} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-135} & & \\\Leftrightarrow & x = \frac{-112}{135} & & \\ & V = \left\{ \frac{-112}{135} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+36} & = & \color{red}{45x} +50 \\\Leftrightarrow & 300x \color{red}{+36} \color{blue}{-36} \color{blue}{-45x} & = & \color{red}{45x} +50 \color{blue}{-45x} \color{blue}{-36} \\\Leftrightarrow & 300x-45x& = & 50-36 \\\Leftrightarrow & \color{red}{255} x& = & 14 \\\Leftrightarrow & x = \frac{14}{255} & & \\ & V = \left\{ \frac{14}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{-84} & = & \color{red}{175x} +50 \\\Leftrightarrow & 840x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 840x-175x& = & 50+84 \\\Leftrightarrow & \color{red}{665} x& = & 134 \\\Leftrightarrow & x = \frac{134}{665} & & \\ & V = \left\{ \frac{134}{665} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{2})& = & -3x+\frac{9}{10} \\\Leftrightarrow & -28x+\frac{35}{2}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x+ \frac{175}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{+175} & = & \color{red}{-30x} +9 \\\Leftrightarrow & -280x \color{red}{+175} \color{blue}{-175} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{-175} \\\Leftrightarrow & -280x+30x& = & 9-175 \\\Leftrightarrow & \color{red}{-250} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-250} & & \\\Leftrightarrow & x = \frac{83}{125} & & \\ & V = \left\{ \frac{83}{125} \right\} & \\\end{align}\)