Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-270} & = & \color{red}{-441x} +56 \\\Leftrightarrow & -1890x \color{red}{-270} \color{blue}{+270} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{+270} \\\Leftrightarrow & -1890x+441x& = & 56+270 \\\Leftrightarrow & \color{red}{-1449} x& = & 326 \\\Leftrightarrow & x = \frac{326}{-1449} & & \\\Leftrightarrow & x = \frac{-326}{1449} & & \\ & V = \left\{ \frac{-326}{1449} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{7})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 8x-\frac{10}{7}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{-20} & = & \color{red}{-42x} +21 \\\Leftrightarrow & 112x \color{red}{-20} \color{blue}{+20} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{+20} \\\Leftrightarrow & 112x+42x& = & 21+20 \\\Leftrightarrow & \color{red}{154} x& = & 41 \\\Leftrightarrow & x = \frac{41}{154} & & \\ & V = \left\{ \frac{41}{154} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{5})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 28x+\frac{21}{5}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{980}{ \color{blue}{35} }x+ \frac{147}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 980x \color{red}{+147} & = & \color{red}{-175x} +45 \\\Leftrightarrow & 980x \color{red}{+147} \color{blue}{-147} \color{blue}{+175x} & = & \color{red}{-175x} +45 \color{blue}{+175x} \color{blue}{-147} \\\Leftrightarrow & 980x+175x& = & 45-147 \\\Leftrightarrow & \color{red}{1155} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{1155} & & \\\Leftrightarrow & x = \frac{-34}{385} & & \\ & V = \left\{ \frac{-34}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{4}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{105x} +10 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-12} \\\Leftrightarrow & 120x-105x& = & 10-12 \\\Leftrightarrow & \color{red}{15} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{25}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{125}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-125} & = & \color{red}{105x} +18 \\\Leftrightarrow & -300x \color{red}{-125} \color{blue}{+125} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{+125} \\\Leftrightarrow & -300x-105x& = & 18+125 \\\Leftrightarrow & \color{red}{-405} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-405} & & \\\Leftrightarrow & x = \frac{-143}{405} & & \\ & V = \left\{ \frac{-143}{405} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{4})& = & -9x+\frac{5}{6} \\\Leftrightarrow & 35x-\frac{21}{4}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x- \frac{63}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{-63} & = & \color{red}{-108x} +10 \\\Leftrightarrow & 420x \color{red}{-63} \color{blue}{+63} \color{blue}{+108x} & = & \color{red}{-108x} +10 \color{blue}{+108x} \color{blue}{+63} \\\Leftrightarrow & 420x+108x& = & 10+63 \\\Leftrightarrow & \color{red}{528} x& = & 73 \\\Leftrightarrow & x = \frac{73}{528} & & \\ & V = \left\{ \frac{73}{528} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & -2x+\frac{3}{4} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{-48} & = & \color{red}{-40x} +15 \\\Leftrightarrow & 180x \color{red}{-48} \color{blue}{+48} \color{blue}{+40x} & = & \color{red}{-40x} +15 \color{blue}{+40x} \color{blue}{+48} \\\Leftrightarrow & 180x+40x& = & 15+48 \\\Leftrightarrow & \color{red}{220} x& = & 63 \\\Leftrightarrow & x = \frac{63}{220} & & \\ & V = \left\{ \frac{63}{220} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{8}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+8} & = & \color{red}{45x} +6 \\\Leftrightarrow & 108x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & 108x-45x& = & 6-8 \\\Leftrightarrow & \color{red}{63} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{63} & & \\ & V = \left\{ \frac{-2}{63} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{-60} & = & \color{red}{154x} +99 \\\Leftrightarrow & -660x \color{red}{-60} \color{blue}{+60} \color{blue}{-154x} & = & \color{red}{154x} +99 \color{blue}{-154x} \color{blue}{+60} \\\Leftrightarrow & -660x-154x& = & 99+60 \\\Leftrightarrow & \color{red}{-814} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-814} & & \\\Leftrightarrow & x = \frac{-159}{814} & & \\ & V = \left\{ \frac{-159}{814} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-108} & = & \color{red}{-315x} +40 \\\Leftrightarrow & 540x \color{red}{-108} \color{blue}{+108} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{+108} \\\Leftrightarrow & 540x+315x& = & 40+108 \\\Leftrightarrow & \color{red}{855} x& = & 148 \\\Leftrightarrow & x = \frac{148}{855} & & \\ & V = \left\{ \frac{148}{855} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{3})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -16x-\frac{8}{3}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{-80} & = & \color{red}{-210x} +21 \\\Leftrightarrow & -480x \color{red}{-80} \color{blue}{+80} \color{blue}{+210x} & = & \color{red}{-210x} +21 \color{blue}{+210x} \color{blue}{+80} \\\Leftrightarrow & -480x+210x& = & 21+80 \\\Leftrightarrow & \color{red}{-270} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-270} & & \\\Leftrightarrow & x = \frac{-101}{270} & & \\ & V = \left\{ \frac{-101}{270} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{4})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -10x-\frac{25}{4}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{175}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-175} & = & \color{red}{196x} +32 \\\Leftrightarrow & -280x \color{red}{-175} \color{blue}{+175} \color{blue}{-196x} & = & \color{red}{196x} +32 \color{blue}{-196x} \color{blue}{+175} \\\Leftrightarrow & -280x-196x& = & 32+175 \\\Leftrightarrow & \color{red}{-476} x& = & 207 \\\Leftrightarrow & x = \frac{207}{-476} & & \\\Leftrightarrow & x = \frac{-207}{476} & & \\ & V = \left\{ \frac{-207}{476} \right\} & \\\end{align}\)