Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{7})& = & -5x+\frac{5}{4} \\\Leftrightarrow & 12x-\frac{12}{7}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x- \frac{48}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{-48} & = & \color{red}{-140x} +35 \\\Leftrightarrow & 336x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +35 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & 336x+140x& = & 35+48 \\\Leftrightarrow & \color{red}{476} x& = & 83 \\\Leftrightarrow & x = \frac{83}{476} & & \\ & V = \left\{ \frac{83}{476} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{11})& = & -4x+\frac{7}{3} \\\Leftrightarrow & 15x-\frac{6}{11}& = & -4x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-18} & = & \color{red}{-132x} +77 \\\Leftrightarrow & 495x \color{red}{-18} \color{blue}{+18} \color{blue}{+132x} & = & \color{red}{-132x} +77 \color{blue}{+132x} \color{blue}{+18} \\\Leftrightarrow & 495x+132x& = & 77+18 \\\Leftrightarrow & \color{red}{627} x& = & 95 \\\Leftrightarrow & x = \frac{95}{627} & & \\\Leftrightarrow & x = \frac{5}{33} & & \\ & V = \left\{ \frac{5}{33} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{15}{4}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{+105} & = & \color{red}{196x} +40 \\\Leftrightarrow & -280x \color{red}{+105} \color{blue}{-105} \color{blue}{-196x} & = & \color{red}{196x} +40 \color{blue}{-196x} \color{blue}{-105} \\\Leftrightarrow & -280x-196x& = & 40-105 \\\Leftrightarrow & \color{red}{-476} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-476} & & \\\Leftrightarrow & x = \frac{65}{476} & & \\ & V = \left\{ \frac{65}{476} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-110} & = & \color{red}{-385x} +70 \\\Leftrightarrow & 462x \color{red}{-110} \color{blue}{+110} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{+110} \\\Leftrightarrow & 462x+385x& = & 70+110 \\\Leftrightarrow & \color{red}{847} x& = & 180 \\\Leftrightarrow & x = \frac{180}{847} & & \\ & V = \left\{ \frac{180}{847} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-98} & = & \color{red}{63x} +18 \\\Leftrightarrow & 588x \color{red}{-98} \color{blue}{+98} \color{blue}{-63x} & = & \color{red}{63x} +18 \color{blue}{-63x} \color{blue}{+98} \\\Leftrightarrow & 588x-63x& = & 18+98 \\\Leftrightarrow & \color{red}{525} x& = & 116 \\\Leftrightarrow & x = \frac{116}{525} & & \\ & V = \left\{ \frac{116}{525} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{3})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 28x-\frac{28}{3}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{-28} & = & \color{red}{9x} +4 \\\Leftrightarrow & 84x \color{red}{-28} \color{blue}{+28} \color{blue}{-9x} & = & \color{red}{9x} +4 \color{blue}{-9x} \color{blue}{+28} \\\Leftrightarrow & 84x-9x& = & 4+28 \\\Leftrightarrow & \color{red}{75} x& = & 32 \\\Leftrightarrow & x = \frac{32}{75} & & \\ & V = \left\{ \frac{32}{75} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{7})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{-20} & = & \color{red}{42x} +49 \\\Leftrightarrow & 112x \color{red}{-20} \color{blue}{+20} \color{blue}{-42x} & = & \color{red}{42x} +49 \color{blue}{-42x} \color{blue}{+20} \\\Leftrightarrow & 112x-42x& = & 49+20 \\\Leftrightarrow & \color{red}{70} x& = & 69 \\\Leftrightarrow & x = \frac{69}{70} & & \\ & V = \left\{ \frac{69}{70} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{12}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-60} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -660x \color{red}{-60} \color{blue}{+60} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+60} \\\Leftrightarrow & -660x+275x& = & 66+60 \\\Leftrightarrow & \color{red}{-385} x& = & 126 \\\Leftrightarrow & x = \frac{126}{-385} & & \\\Leftrightarrow & x = \frac{-18}{55} & & \\ & V = \left\{ \frac{-18}{55} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{5})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{8}{5}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{-45x} +10 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{-24} \\\Leftrightarrow & 120x+45x& = & 10-24 \\\Leftrightarrow & \color{red}{165} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{165} & & \\ & V = \left\{ \frac{-14}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{9})& = & -9x+\frac{10}{9} \\\Leftrightarrow & 14x-\frac{35}{9}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-35} & = & \color{red}{-81x} +10 \\\Leftrightarrow & 126x \color{red}{-35} \color{blue}{+35} \color{blue}{+81x} & = & \color{red}{-81x} +10 \color{blue}{+81x} \color{blue}{+35} \\\Leftrightarrow & 126x+81x& = & 10+35 \\\Leftrightarrow & \color{red}{207} x& = & 45 \\\Leftrightarrow & x = \frac{45}{207} & & \\\Leftrightarrow & x = \frac{5}{23} & & \\ & V = \left\{ \frac{5}{23} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 4x+\frac{6}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{+54} & = & \color{red}{495x} +88 \\\Leftrightarrow & 396x \color{red}{+54} \color{blue}{-54} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{-54} \\\Leftrightarrow & 396x-495x& = & 88-54 \\\Leftrightarrow & \color{red}{-99} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-99} & & \\\Leftrightarrow & x = \frac{-34}{99} & & \\ & V = \left\{ \frac{-34}{99} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -9x+\frac{15}{4}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-72}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -72x \color{red}{+30} & = & \color{red}{-40x} +7 \\\Leftrightarrow & -72x \color{red}{+30} \color{blue}{-30} \color{blue}{+40x} & = & \color{red}{-40x} +7 \color{blue}{+40x} \color{blue}{-30} \\\Leftrightarrow & -72x+40x& = & 7-30 \\\Leftrightarrow & \color{red}{-32} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-32} & & \\\Leftrightarrow & x = \frac{23}{32} & & \\ & V = \left\{ \frac{23}{32} \right\} & \\\end{align}\)