Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{24}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x+ \frac{72}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{+72} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 630x \color{red}{+72} \color{blue}{-72} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-72} \\\Leftrightarrow & 630x+147x& = & 14-72 \\\Leftrightarrow & \color{red}{777} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{777} & & \\ & V = \left\{ \frac{-58}{777} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & -2x+\frac{9}{5} \\\Leftrightarrow & 9x-\frac{6}{7}& = & -2x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{-30} & = & \color{red}{-70x} +63 \\\Leftrightarrow & 315x \color{red}{-30} \color{blue}{+30} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+30} \\\Leftrightarrow & 315x+70x& = & 63+30 \\\Leftrightarrow & \color{red}{385} x& = & 93 \\\Leftrightarrow & x = \frac{93}{385} & & \\ & V = \left\{ \frac{93}{385} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{5})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+168} & = & \color{red}{175x} +45 \\\Leftrightarrow & -840x \color{red}{+168} \color{blue}{-168} \color{blue}{-175x} & = & \color{red}{175x} +45 \color{blue}{-175x} \color{blue}{-168} \\\Leftrightarrow & -840x-175x& = & 45-168 \\\Leftrightarrow & \color{red}{-1015} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{-1015} & & \\\Leftrightarrow & x = \frac{123}{1015} & & \\ & V = \left\{ \frac{123}{1015} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{7})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 6x+\frac{9}{7}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{+72} & = & \color{red}{392x} +63 \\\Leftrightarrow & 336x \color{red}{+72} \color{blue}{-72} \color{blue}{-392x} & = & \color{red}{392x} +63 \color{blue}{-392x} \color{blue}{-72} \\\Leftrightarrow & 336x-392x& = & 63-72 \\\Leftrightarrow & \color{red}{-56} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-56} & & \\\Leftrightarrow & x = \frac{9}{56} & & \\ & V = \left\{ \frac{9}{56} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{9})& = & 8x+\frac{5}{3} \\\Leftrightarrow & 21x+\frac{14}{9}& = & 8x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{14}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+14} & = & \color{red}{72x} +15 \\\Leftrightarrow & 189x \color{red}{+14} \color{blue}{-14} \color{blue}{-72x} & = & \color{red}{72x} +15 \color{blue}{-72x} \color{blue}{-14} \\\Leftrightarrow & 189x-72x& = & 15-14 \\\Leftrightarrow & \color{red}{117} x& = & 1 \\\Leftrightarrow & x = \frac{1}{117} & & \\ & V = \left\{ \frac{1}{117} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1260}{ \color{blue}{42} }x- \frac{180}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1260x \color{red}{-180} & = & \color{red}{294x} +35 \\\Leftrightarrow & 1260x \color{red}{-180} \color{blue}{+180} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{+180} \\\Leftrightarrow & 1260x-294x& = & 35+180 \\\Leftrightarrow & \color{red}{966} x& = & 215 \\\Leftrightarrow & x = \frac{215}{966} & & \\ & V = \left\{ \frac{215}{966} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{8})& = & -2x+\frac{5}{12} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -2x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{-48x} +10 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{+48x} & = & \color{red}{-48x} +10 \color{blue}{+48x} \color{blue}{-63} \\\Leftrightarrow & -672x+48x& = & 10-63 \\\Leftrightarrow & \color{red}{-624} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-624} & & \\\Leftrightarrow & x = \frac{53}{624} & & \\ & V = \left\{ \frac{53}{624} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{11})& = & -8x+\frac{8}{7} \\\Leftrightarrow & 25x-\frac{15}{11}& = & -8x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{105}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-105} & = & \color{red}{-616x} +88 \\\Leftrightarrow & 1925x \color{red}{-105} \color{blue}{+105} \color{blue}{+616x} & = & \color{red}{-616x} +88 \color{blue}{+616x} \color{blue}{+105} \\\Leftrightarrow & 1925x+616x& = & 88+105 \\\Leftrightarrow & \color{red}{2541} x& = & 193 \\\Leftrightarrow & x = \frac{193}{2541} & & \\ & V = \left\{ \frac{193}{2541} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-90} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & -1320x+275x& = & 66+90 \\\Leftrightarrow & \color{red}{-1045} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-1045} & & \\\Leftrightarrow & x = \frac{-156}{1045} & & \\ & V = \left\{ \frac{-156}{1045} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{12}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{108}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+108} & = & \color{red}{-315x} +70 \\\Leftrightarrow & -756x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -756x+315x& = & 70-108 \\\Leftrightarrow & \color{red}{-441} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-441} & & \\\Leftrightarrow & x = \frac{38}{441} & & \\ & V = \left\{ \frac{38}{441} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{7})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -30x-\frac{12}{7}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1680}{ \color{blue}{56} }x- \frac{96}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1680x \color{red}{-96} & = & \color{red}{-392x} +49 \\\Leftrightarrow & -1680x \color{red}{-96} \color{blue}{+96} \color{blue}{+392x} & = & \color{red}{-392x} +49 \color{blue}{+392x} \color{blue}{+96} \\\Leftrightarrow & -1680x+392x& = & 49+96 \\\Leftrightarrow & \color{red}{-1288} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-1288} & & \\\Leftrightarrow & x = \frac{-145}{1288} & & \\ & V = \left\{ \frac{-145}{1288} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{11})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 12x+\frac{6}{11}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+42} & = & \color{red}{-385x} +99 \\\Leftrightarrow & 924x \color{red}{+42} \color{blue}{-42} \color{blue}{+385x} & = & \color{red}{-385x} +99 \color{blue}{+385x} \color{blue}{-42} \\\Leftrightarrow & 924x+385x& = & 99-42 \\\Leftrightarrow & \color{red}{1309} x& = & 57 \\\Leftrightarrow & x = \frac{57}{1309} & & \\ & V = \left\{ \frac{57}{1309} \right\} & \\\end{align}\)