Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{3})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -28x+\frac{35}{3}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{+35} & = & \color{red}{-15x} +2 \\\Leftrightarrow & -84x \color{red}{+35} \color{blue}{-35} \color{blue}{+15x} & = & \color{red}{-15x} +2 \color{blue}{+15x} \color{blue}{-35} \\\Leftrightarrow & -84x+15x& = & 2-35 \\\Leftrightarrow & \color{red}{-69} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-69} & & \\\Leftrightarrow & x = \frac{11}{23} & & \\ & V = \left\{ \frac{11}{23} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{+147} & = & \color{red}{-224x} +80 \\\Leftrightarrow & 1176x \color{red}{+147} \color{blue}{-147} \color{blue}{+224x} & = & \color{red}{-224x} +80 \color{blue}{+224x} \color{blue}{-147} \\\Leftrightarrow & 1176x+224x& = & 80-147 \\\Leftrightarrow & \color{red}{1400} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{1400} & & \\ & V = \left\{ \frac{-67}{1400} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{9})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -28x-\frac{35}{9}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-1008}{ \color{blue}{36} }x- \frac{140}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -1008x \color{red}{-140} & = & \color{red}{324x} +81 \\\Leftrightarrow & -1008x \color{red}{-140} \color{blue}{+140} \color{blue}{-324x} & = & \color{red}{324x} +81 \color{blue}{-324x} \color{blue}{+140} \\\Leftrightarrow & -1008x-324x& = & 81+140 \\\Leftrightarrow & \color{red}{-1332} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-1332} & & \\\Leftrightarrow & x = \frac{-221}{1332} & & \\ & V = \left\{ \frac{-221}{1332} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x-\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-36} & = & \color{red}{105x} +10 \\\Leftrightarrow & -90x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -90x-105x& = & 10+36 \\\Leftrightarrow & \color{red}{-195} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-195} & & \\\Leftrightarrow & x = \frac{-46}{195} & & \\ & V = \left\{ \frac{-46}{195} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{20}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+60} & = & \color{red}{105x} +14 \\\Leftrightarrow & 252x \color{red}{+60} \color{blue}{-60} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{-60} \\\Leftrightarrow & 252x-105x& = & 14-60 \\\Leftrightarrow & \color{red}{147} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{147} & & \\ & V = \left\{ \frac{-46}{147} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{-36} & = & \color{red}{105x} +50 \\\Leftrightarrow & -450x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -450x-105x& = & 50+36 \\\Leftrightarrow & \color{red}{-555} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-555} & & \\\Leftrightarrow & x = \frac{-86}{555} & & \\ & V = \left\{ \frac{-86}{555} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & -4x+\frac{2}{3} \\\Leftrightarrow & 15x+\frac{9}{5}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+27} & = & \color{red}{-60x} +10 \\\Leftrightarrow & 225x \color{red}{+27} \color{blue}{-27} \color{blue}{+60x} & = & \color{red}{-60x} +10 \color{blue}{+60x} \color{blue}{-27} \\\Leftrightarrow & 225x+60x& = & 10-27 \\\Leftrightarrow & \color{red}{285} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{285} & & \\ & V = \left\{ \frac{-17}{285} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{3})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{25}{3}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x- \frac{125}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{-125} & = & \color{red}{-30x} +18 \\\Leftrightarrow & 225x \color{red}{-125} \color{blue}{+125} \color{blue}{+30x} & = & \color{red}{-30x} +18 \color{blue}{+30x} \color{blue}{+125} \\\Leftrightarrow & 225x+30x& = & 18+125 \\\Leftrightarrow & \color{red}{255} x& = & 143 \\\Leftrightarrow & x = \frac{143}{255} & & \\ & V = \left\{ \frac{143}{255} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{5})& = & 3x+\frac{2}{5} \\\Leftrightarrow & 20x-\frac{12}{5}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{-12} & = & \color{red}{15x} +2 \\\Leftrightarrow & 100x \color{red}{-12} \color{blue}{+12} \color{blue}{-15x} & = & \color{red}{15x} +2 \color{blue}{-15x} \color{blue}{+12} \\\Leftrightarrow & 100x-15x& = & 2+12 \\\Leftrightarrow & \color{red}{85} x& = & 14 \\\Leftrightarrow & x = \frac{14}{85} & & \\ & V = \left\{ \frac{14}{85} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{11})& = & 7x+\frac{7}{9} \\\Leftrightarrow & 16x-\frac{8}{11}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x- \frac{72}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{-72} & = & \color{red}{693x} +77 \\\Leftrightarrow & 1584x \color{red}{-72} \color{blue}{+72} \color{blue}{-693x} & = & \color{red}{693x} +77 \color{blue}{-693x} \color{blue}{+72} \\\Leftrightarrow & 1584x-693x& = & 77+72 \\\Leftrightarrow & \color{red}{891} x& = & 149 \\\Leftrightarrow & x = \frac{149}{891} & & \\ & V = \left\{ \frac{149}{891} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{3})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 16x-\frac{8}{3}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-56} & = & \color{red}{63x} +12 \\\Leftrightarrow & 336x \color{red}{-56} \color{blue}{+56} \color{blue}{-63x} & = & \color{red}{63x} +12 \color{blue}{-63x} \color{blue}{+56} \\\Leftrightarrow & 336x-63x& = & 12+56 \\\Leftrightarrow & \color{red}{273} x& = & 68 \\\Leftrightarrow & x = \frac{68}{273} & & \\ & V = \left\{ \frac{68}{273} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-72}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{-90x} +15 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{+90x} & = & \color{red}{-90x} +15 \color{blue}{+90x} \color{blue}{+16} \\\Leftrightarrow & -72x+90x& = & 15+16 \\\Leftrightarrow & \color{red}{18} x& = & 31 \\\Leftrightarrow & x = \frac{31}{18} & & \\ & V = \left\{ \frac{31}{18} \right\} & \\\end{align}\)