Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+90} & = & \color{red}{385x} +66 \\\Leftrightarrow & -1650x \color{red}{+90} \color{blue}{-90} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-90} \\\Leftrightarrow & -1650x-385x& = & 66-90 \\\Leftrightarrow & \color{red}{-2035} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-2035} & & \\\Leftrightarrow & x = \frac{24}{2035} & & \\ & V = \left\{ \frac{24}{2035} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 40-36 \\\Leftrightarrow & \color{red}{255} x& = & 4 \\\Leftrightarrow & x = \frac{4}{255} & & \\ & V = \left\{ \frac{4}{255} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{11})& = & -2x+\frac{9}{5} \\\Leftrightarrow & 9x+\frac{15}{11}& = & -2x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{+75} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 495x \color{red}{+75} \color{blue}{-75} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{-75} \\\Leftrightarrow & 495x+110x& = & 99-75 \\\Leftrightarrow & \color{red}{605} x& = & 24 \\\Leftrightarrow & x = \frac{24}{605} & & \\ & V = \left\{ \frac{24}{605} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 4x-\frac{8}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x- \frac{24}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{75x} +20 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+24} \\\Leftrightarrow & 60x-75x& = & 20+24 \\\Leftrightarrow & \color{red}{-15} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-15} & & \\\Leftrightarrow & x = \frac{-44}{15} & & \\ & V = \left\{ \frac{-44}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{11})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -18x+\frac{24}{11}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-792}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -792x \color{red}{+96} & = & \color{red}{396x} +33 \\\Leftrightarrow & -792x \color{red}{+96} \color{blue}{-96} \color{blue}{-396x} & = & \color{red}{396x} +33 \color{blue}{-396x} \color{blue}{-96} \\\Leftrightarrow & -792x-396x& = & 33-96 \\\Leftrightarrow & \color{red}{-1188} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-1188} & & \\\Leftrightarrow & x = \frac{7}{132} & & \\ & V = \left\{ \frac{7}{132} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{4})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-105} & = & \color{red}{140x} +24 \\\Leftrightarrow & -336x \color{red}{-105} \color{blue}{+105} \color{blue}{-140x} & = & \color{red}{140x} +24 \color{blue}{-140x} \color{blue}{+105} \\\Leftrightarrow & -336x-140x& = & 24+105 \\\Leftrightarrow & \color{red}{-476} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-476} & & \\\Leftrightarrow & x = \frac{-129}{476} & & \\ & V = \left\{ \frac{-129}{476} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+1)& = & -8x+\frac{2}{3} \\\Leftrightarrow & -21x-7& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x- \frac{21}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{-21} & = & \color{red}{-24x} +2 \\\Leftrightarrow & -63x \color{red}{-21} \color{blue}{+21} \color{blue}{+24x} & = & \color{red}{-24x} +2 \color{blue}{+24x} \color{blue}{+21} \\\Leftrightarrow & -63x+24x& = & 2+21 \\\Leftrightarrow & \color{red}{-39} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-39} & & \\\Leftrightarrow & x = \frac{-23}{39} & & \\ & V = \left\{ \frac{-23}{39} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & 7x+\frac{7}{9} \\\Leftrightarrow & 30x-\frac{18}{5}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x- \frac{162}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{-162} & = & \color{red}{315x} +35 \\\Leftrightarrow & 1350x \color{red}{-162} \color{blue}{+162} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{+162} \\\Leftrightarrow & 1350x-315x& = & 35+162 \\\Leftrightarrow & \color{red}{1035} x& = & 197 \\\Leftrightarrow & x = \frac{197}{1035} & & \\ & V = \left\{ \frac{197}{1035} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{5}{4} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-56} & = & \color{red}{-96x} +15 \\\Leftrightarrow & -252x \color{red}{-56} \color{blue}{+56} \color{blue}{+96x} & = & \color{red}{-96x} +15 \color{blue}{+96x} \color{blue}{+56} \\\Leftrightarrow & -252x+96x& = & 15+56 \\\Leftrightarrow & \color{red}{-156} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-156} & & \\\Leftrightarrow & x = \frac{-71}{156} & & \\ & V = \left\{ \frac{-71}{156} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{7})& = & -4x+\frac{3}{8} \\\Leftrightarrow & 25x+\frac{20}{7}& = & -4x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1400}{ \color{blue}{56} }x+ \frac{160}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1400x \color{red}{+160} & = & \color{red}{-224x} +21 \\\Leftrightarrow & 1400x \color{red}{+160} \color{blue}{-160} \color{blue}{+224x} & = & \color{red}{-224x} +21 \color{blue}{+224x} \color{blue}{-160} \\\Leftrightarrow & 1400x+224x& = & 21-160 \\\Leftrightarrow & \color{red}{1624} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{1624} & & \\ & V = \left\{ \frac{-139}{1624} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{7})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-112}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -112x \color{red}{-24} & = & \color{red}{-252x} +21 \\\Leftrightarrow & -112x \color{red}{-24} \color{blue}{+24} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{+24} \\\Leftrightarrow & -112x+252x& = & 21+24 \\\Leftrightarrow & \color{red}{140} x& = & 45 \\\Leftrightarrow & x = \frac{45}{140} & & \\\Leftrightarrow & x = \frac{9}{28} & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{7})& = & -8x+\frac{3}{5} \\\Leftrightarrow & -25x+\frac{25}{7}& = & -8x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{125}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+125} & = & \color{red}{-280x} +21 \\\Leftrightarrow & -875x \color{red}{+125} \color{blue}{-125} \color{blue}{+280x} & = & \color{red}{-280x} +21 \color{blue}{+280x} \color{blue}{-125} \\\Leftrightarrow & -875x+280x& = & 21-125 \\\Leftrightarrow & \color{red}{-595} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-595} & & \\\Leftrightarrow & x = \frac{104}{595} & & \\ & V = \left\{ \frac{104}{595} \right\} & \\\end{align}\)