Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{7})& = & -3x+\frac{7}{3} \\\Leftrightarrow & 10x+\frac{20}{7}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+60} & = & \color{red}{-63x} +49 \\\Leftrightarrow & 210x \color{red}{+60} \color{blue}{-60} \color{blue}{+63x} & = & \color{red}{-63x} +49 \color{blue}{+63x} \color{blue}{-60} \\\Leftrightarrow & 210x+63x& = & 49-60 \\\Leftrightarrow & \color{red}{273} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{273} & & \\ & V = \left\{ \frac{-11}{273} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{5})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -12x-\frac{24}{5}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-168} & = & \color{red}{-175x} +45 \\\Leftrightarrow & -420x \color{red}{-168} \color{blue}{+168} \color{blue}{+175x} & = & \color{red}{-175x} +45 \color{blue}{+175x} \color{blue}{+168} \\\Leftrightarrow & -420x+175x& = & 45+168 \\\Leftrightarrow & \color{red}{-245} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-245} & & \\\Leftrightarrow & x = \frac{-213}{245} & & \\ & V = \left\{ \frac{-213}{245} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 18x-\frac{24}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{+72} \\\Leftrightarrow & 270x+75x& = & 40+72 \\\Leftrightarrow & \color{red}{345} x& = & 112 \\\Leftrightarrow & x = \frac{112}{345} & & \\ & V = \left\{ \frac{112}{345} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{+24} & = & \color{red}{-50x} +9 \\\Leftrightarrow & 240x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & 240x+50x& = & 9-24 \\\Leftrightarrow & \color{red}{290} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{290} & & \\\Leftrightarrow & x = \frac{-3}{58} & & \\ & V = \left\{ \frac{-3}{58} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{7})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{15}{7}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-165} & = & \color{red}{385x} +14 \\\Leftrightarrow & 462x \color{red}{-165} \color{blue}{+165} \color{blue}{-385x} & = & \color{red}{385x} +14 \color{blue}{-385x} \color{blue}{+165} \\\Leftrightarrow & 462x-385x& = & 14+165 \\\Leftrightarrow & \color{red}{77} x& = & 179 \\\Leftrightarrow & x = \frac{179}{77} & & \\ & V = \left\{ \frac{179}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & -330x+231x& = & 110+30 \\\Leftrightarrow & \color{red}{-99} x& = & 140 \\\Leftrightarrow & x = \frac{140}{-99} & & \\\Leftrightarrow & x = \frac{-140}{99} & & \\ & V = \left\{ \frac{-140}{99} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 18x-\frac{24}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-264} & = & \color{red}{-275x} +25 \\\Leftrightarrow & 990x \color{red}{-264} \color{blue}{+264} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{+264} \\\Leftrightarrow & 990x+275x& = & 25+264 \\\Leftrightarrow & \color{red}{1265} x& = & 289 \\\Leftrightarrow & x = \frac{289}{1265} & & \\ & V = \left\{ \frac{289}{1265} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -24x-\frac{30}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{-270} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -1512x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & -1512x+315x& = & 56+270 \\\Leftrightarrow & \color{red}{-1197} x& = & 326 \\\Leftrightarrow & x = \frac{326}{-1197} & & \\\Leftrightarrow & x = \frac{-326}{1197} & & \\ & V = \left\{ \frac{-326}{1197} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{7})& = & -8x+\frac{7}{3} \\\Leftrightarrow & 15x+\frac{9}{7}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+27} & = & \color{red}{-168x} +49 \\\Leftrightarrow & 315x \color{red}{+27} \color{blue}{-27} \color{blue}{+168x} & = & \color{red}{-168x} +49 \color{blue}{+168x} \color{blue}{-27} \\\Leftrightarrow & 315x+168x& = & 49-27 \\\Leftrightarrow & \color{red}{483} x& = & 22 \\\Leftrightarrow & x = \frac{22}{483} & & \\ & V = \left\{ \frac{22}{483} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -12x+\frac{20}{3}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-72}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -72x \color{red}{+40} & = & \color{red}{30x} +5 \\\Leftrightarrow & -72x \color{red}{+40} \color{blue}{-40} \color{blue}{-30x} & = & \color{red}{30x} +5 \color{blue}{-30x} \color{blue}{-40} \\\Leftrightarrow & -72x-30x& = & 5-40 \\\Leftrightarrow & \color{red}{-102} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-102} & & \\\Leftrightarrow & x = \frac{35}{102} & & \\ & V = \left\{ \frac{35}{102} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 16x+\frac{20}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+60} & = & \color{red}{165x} +110 \\\Leftrightarrow & 528x \color{red}{+60} \color{blue}{-60} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{-60} \\\Leftrightarrow & 528x-165x& = & 110-60 \\\Leftrightarrow & \color{red}{363} x& = & 50 \\\Leftrightarrow & x = \frac{50}{363} & & \\ & V = \left\{ \frac{50}{363} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{3})& = & -8x+\frac{4}{9} \\\Leftrightarrow & -21x-\frac{28}{3}& = & -8x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{84}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-84} & = & \color{red}{-72x} +4 \\\Leftrightarrow & -189x \color{red}{-84} \color{blue}{+84} \color{blue}{+72x} & = & \color{red}{-72x} +4 \color{blue}{+72x} \color{blue}{+84} \\\Leftrightarrow & -189x+72x& = & 4+84 \\\Leftrightarrow & \color{red}{-117} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-117} & & \\\Leftrightarrow & x = \frac{-88}{117} & & \\ & V = \left\{ \frac{-88}{117} \right\} & \\\end{align}\)