Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{3})& = & -6x+\frac{2}{5} \\\Leftrightarrow & -28x-\frac{28}{3}& = & -6x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x- \frac{140}{ \color{blue}{15} })& = & (\frac{-90}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{-140} & = & \color{red}{-90x} +6 \\\Leftrightarrow & -420x \color{red}{-140} \color{blue}{+140} \color{blue}{+90x} & = & \color{red}{-90x} +6 \color{blue}{+90x} \color{blue}{+140} \\\Leftrightarrow & -420x+90x& = & 6+140 \\\Leftrightarrow & \color{red}{-330} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-330} & & \\\Leftrightarrow & x = \frac{-73}{165} & & \\ & V = \left\{ \frac{-73}{165} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 28x+\frac{28}{9}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1764}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1764x \color{red}{+196} & = & \color{red}{315x} +45 \\\Leftrightarrow & 1764x \color{red}{+196} \color{blue}{-196} \color{blue}{-315x} & = & \color{red}{315x} +45 \color{blue}{-315x} \color{blue}{-196} \\\Leftrightarrow & 1764x-315x& = & 45-196 \\\Leftrightarrow & \color{red}{1449} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{1449} & & \\ & V = \left\{ \frac{-151}{1449} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{3})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{20}{3}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+100} & = & \color{red}{75x} +18 \\\Leftrightarrow & 180x \color{red}{+100} \color{blue}{-100} \color{blue}{-75x} & = & \color{red}{75x} +18 \color{blue}{-75x} \color{blue}{-100} \\\Leftrightarrow & 180x-75x& = & 18-100 \\\Leftrightarrow & \color{red}{105} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{105} & & \\ & V = \left\{ \frac{-82}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{9})& = & -8x+\frac{4}{3} \\\Leftrightarrow & 21x-\frac{35}{9}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{-35} & = & \color{red}{-72x} +12 \\\Leftrightarrow & 189x \color{red}{-35} \color{blue}{+35} \color{blue}{+72x} & = & \color{red}{-72x} +12 \color{blue}{+72x} \color{blue}{+35} \\\Leftrightarrow & 189x+72x& = & 12+35 \\\Leftrightarrow & \color{red}{261} x& = & 47 \\\Leftrightarrow & x = \frac{47}{261} & & \\ & V = \left\{ \frac{47}{261} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{105x} +56 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & -84x-105x& = & 56-18 \\\Leftrightarrow & \color{red}{-189} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-189} & & \\\Leftrightarrow & x = \frac{-38}{189} & & \\ & V = \left\{ \frac{-38}{189} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -9x+\frac{2}{5} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{+30} & = & \color{red}{-315x} +14 \\\Leftrightarrow & 140x \color{red}{+30} \color{blue}{-30} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{-30} \\\Leftrightarrow & 140x+315x& = & 14-30 \\\Leftrightarrow & \color{red}{455} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{455} & & \\ & V = \left\{ \frac{-16}{455} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{24}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-120} & = & \color{red}{385x} +66 \\\Leftrightarrow & -1650x \color{red}{-120} \color{blue}{+120} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+120} \\\Leftrightarrow & -1650x-385x& = & 66+120 \\\Leftrightarrow & \color{red}{-2035} x& = & 186 \\\Leftrightarrow & x = \frac{186}{-2035} & & \\\Leftrightarrow & x = \frac{-186}{2035} & & \\ & V = \left\{ \frac{-186}{2035} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{3})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 4x+\frac{8}{3}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+56} & = & \color{red}{147x} +24 \\\Leftrightarrow & 84x \color{red}{+56} \color{blue}{-56} \color{blue}{-147x} & = & \color{red}{147x} +24 \color{blue}{-147x} \color{blue}{-56} \\\Leftrightarrow & 84x-147x& = & 24-56 \\\Leftrightarrow & \color{red}{-63} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-63} & & \\\Leftrightarrow & x = \frac{32}{63} & & \\ & V = \left\{ \frac{32}{63} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{2})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 6x+\frac{15}{2}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{+105} & = & \color{red}{-70x} +12 \\\Leftrightarrow & 84x \color{red}{+105} \color{blue}{-105} \color{blue}{+70x} & = & \color{red}{-70x} +12 \color{blue}{+70x} \color{blue}{-105} \\\Leftrightarrow & 84x+70x& = & 12-105 \\\Leftrightarrow & \color{red}{154} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{154} & & \\ & V = \left\{ \frac{-93}{154} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 6x+\frac{10}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+90} & = & \color{red}{693x} +44 \\\Leftrightarrow & 594x \color{red}{+90} \color{blue}{-90} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{-90} \\\Leftrightarrow & 594x-693x& = & 44-90 \\\Leftrightarrow & \color{red}{-99} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-99} & & \\\Leftrightarrow & x = \frac{46}{99} & & \\ & V = \left\{ \frac{46}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-8} & = & \color{red}{-21x} +2 \\\Leftrightarrow & -60x \color{red}{-8} \color{blue}{+8} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{+8} \\\Leftrightarrow & -60x+21x& = & 2+8 \\\Leftrightarrow & \color{red}{-39} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-39} & & \\\Leftrightarrow & x = \frac{-10}{39} & & \\ & V = \left\{ \frac{-10}{39} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-90} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -252x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & -252x+105x& = & 56+90 \\\Leftrightarrow & \color{red}{-147} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-147} & & \\\Leftrightarrow & x = \frac{-146}{147} & & \\ & V = \left\{ \frac{-146}{147} \right\} & \\\end{align}\)