Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+18} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -90x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -90x+105x& = & 40-18 \\\Leftrightarrow & \color{red}{15} x& = & 22 \\\Leftrightarrow & x = \frac{22}{15} & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{15}{4}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-45} & = & \color{red}{-60x} +16 \\\Leftrightarrow & -144x \color{red}{-45} \color{blue}{+45} \color{blue}{+60x} & = & \color{red}{-60x} +16 \color{blue}{+60x} \color{blue}{+45} \\\Leftrightarrow & -144x+60x& = & 16+45 \\\Leftrightarrow & \color{red}{-84} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-84} & & \\\Leftrightarrow & x = \frac{-61}{84} & & \\ & V = \left\{ \frac{-61}{84} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{7})& = & -3x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{-42x} +49 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{+42x} & = & \color{red}{-42x} +49 \color{blue}{+42x} \color{blue}{+40} \\\Leftrightarrow & -280x+42x& = & 49+40 \\\Leftrightarrow & \color{red}{-238} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-238} & & \\\Leftrightarrow & x = \frac{-89}{238} & & \\ & V = \left\{ \frac{-89}{238} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{9})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-8} & = & \color{red}{81x} +30 \\\Leftrightarrow & -72x \color{red}{-8} \color{blue}{+8} \color{blue}{-81x} & = & \color{red}{81x} +30 \color{blue}{-81x} \color{blue}{+8} \\\Leftrightarrow & -72x-81x& = & 30+8 \\\Leftrightarrow & \color{red}{-153} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-153} & & \\\Leftrightarrow & x = \frac{-38}{153} & & \\ & V = \left\{ \frac{-38}{153} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-48} & = & \color{red}{50x} +9 \\\Leftrightarrow & 120x \color{red}{-48} \color{blue}{+48} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{+48} \\\Leftrightarrow & 120x-50x& = & 9+48 \\\Leftrightarrow & \color{red}{70} x& = & 57 \\\Leftrightarrow & x = \frac{57}{70} & & \\ & V = \left\{ \frac{57}{70} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{5}{9} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-270} & = & \color{red}{-441x} +35 \\\Leftrightarrow & -1890x \color{red}{-270} \color{blue}{+270} \color{blue}{+441x} & = & \color{red}{-441x} +35 \color{blue}{+441x} \color{blue}{+270} \\\Leftrightarrow & -1890x+441x& = & 35+270 \\\Leftrightarrow & \color{red}{-1449} x& = & 305 \\\Leftrightarrow & x = \frac{305}{-1449} & & \\\Leftrightarrow & x = \frac{-305}{1449} & & \\ & V = \left\{ \frac{-305}{1449} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{9})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-40} & = & \color{red}{-225x} +54 \\\Leftrightarrow & 270x \color{red}{-40} \color{blue}{+40} \color{blue}{+225x} & = & \color{red}{-225x} +54 \color{blue}{+225x} \color{blue}{+40} \\\Leftrightarrow & 270x+225x& = & 54+40 \\\Leftrightarrow & \color{red}{495} x& = & 94 \\\Leftrightarrow & x = \frac{94}{495} & & \\ & V = \left\{ \frac{94}{495} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-180} & = & \color{red}{315x} +28 \\\Leftrightarrow & -756x \color{red}{-180} \color{blue}{+180} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{+180} \\\Leftrightarrow & -756x-315x& = & 28+180 \\\Leftrightarrow & \color{red}{-1071} x& = & 208 \\\Leftrightarrow & x = \frac{208}{-1071} & & \\\Leftrightarrow & x = \frac{-208}{1071} & & \\ & V = \left\{ \frac{-208}{1071} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{11})& = & -3x+\frac{3}{5} \\\Leftrightarrow & -8x-\frac{6}{11}& = & -3x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-30} & = & \color{red}{-165x} +33 \\\Leftrightarrow & -440x \color{red}{-30} \color{blue}{+30} \color{blue}{+165x} & = & \color{red}{-165x} +33 \color{blue}{+165x} \color{blue}{+30} \\\Leftrightarrow & -440x+165x& = & 33+30 \\\Leftrightarrow & \color{red}{-275} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-275} & & \\\Leftrightarrow & x = \frac{-63}{275} & & \\ & V = \left\{ \frac{-63}{275} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1080}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1080x \color{red}{-108} & = & \color{red}{-225x} +35 \\\Leftrightarrow & 1080x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +35 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & 1080x+225x& = & 35+108 \\\Leftrightarrow & \color{red}{1305} x& = & 143 \\\Leftrightarrow & x = \frac{143}{1305} & & \\ & V = \left\{ \frac{143}{1305} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{700}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 700x \color{red}{+60} & = & \color{red}{490x} +21 \\\Leftrightarrow & 700x \color{red}{+60} \color{blue}{-60} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{-60} \\\Leftrightarrow & 700x-490x& = & 21-60 \\\Leftrightarrow & \color{red}{210} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{210} & & \\\Leftrightarrow & x = \frac{-13}{70} & & \\ & V = \left\{ \frac{-13}{70} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{3})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -15x+\frac{20}{3}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-45}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -45x \color{red}{+20} & = & \color{red}{12x} +8 \\\Leftrightarrow & -45x \color{red}{+20} \color{blue}{-20} \color{blue}{-12x} & = & \color{red}{12x} +8 \color{blue}{-12x} \color{blue}{-20} \\\Leftrightarrow & -45x-12x& = & 8-20 \\\Leftrightarrow & \color{red}{-57} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-57} & & \\\Leftrightarrow & x = \frac{4}{19} & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)