Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{2})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{15}{2}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+45} & = & \color{red}{-48x} +8 \\\Leftrightarrow & -90x \color{red}{+45} \color{blue}{-45} \color{blue}{+48x} & = & \color{red}{-48x} +8 \color{blue}{+48x} \color{blue}{-45} \\\Leftrightarrow & -90x+48x& = & 8-45 \\\Leftrightarrow & \color{red}{-42} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-42} & & \\\Leftrightarrow & x = \frac{37}{42} & & \\ & V = \left\{ \frac{37}{42} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{5})& = & 3x+\frac{2}{7} \\\Leftrightarrow & -14x+\frac{28}{5}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-490}{ \color{blue}{35} }x+ \frac{196}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -490x \color{red}{+196} & = & \color{red}{105x} +10 \\\Leftrightarrow & -490x \color{red}{+196} \color{blue}{-196} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-196} \\\Leftrightarrow & -490x-105x& = & 10-196 \\\Leftrightarrow & \color{red}{-595} x& = & -186 \\\Leftrightarrow & x = \frac{-186}{-595} & & \\\Leftrightarrow & x = \frac{186}{595} & & \\ & V = \left\{ \frac{186}{595} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{7})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{9}{7}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+99} & = & \color{red}{-616x} +14 \\\Leftrightarrow & -1155x \color{red}{+99} \color{blue}{-99} \color{blue}{+616x} & = & \color{red}{-616x} +14 \color{blue}{+616x} \color{blue}{-99} \\\Leftrightarrow & -1155x+616x& = & 14-99 \\\Leftrightarrow & \color{red}{-539} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-539} & & \\\Leftrightarrow & x = \frac{85}{539} & & \\ & V = \left\{ \frac{85}{539} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+72} & = & \color{red}{105x} +50 \\\Leftrightarrow & -360x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & -360x-105x& = & 50-72 \\\Leftrightarrow & \color{red}{-465} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-465} & & \\\Leftrightarrow & x = \frac{22}{465} & & \\ & V = \left\{ \frac{22}{465} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 120x+75x& = & 10+36 \\\Leftrightarrow & \color{red}{195} x& = & 46 \\\Leftrightarrow & x = \frac{46}{195} & & \\ & V = \left\{ \frac{46}{195} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{5})& = & -8x+\frac{3}{2} \\\Leftrightarrow & 21x-\frac{28}{5}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x- \frac{56}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{-56} & = & \color{red}{-80x} +15 \\\Leftrightarrow & 210x \color{red}{-56} \color{blue}{+56} \color{blue}{+80x} & = & \color{red}{-80x} +15 \color{blue}{+80x} \color{blue}{+56} \\\Leftrightarrow & 210x+80x& = & 15+56 \\\Leftrightarrow & \color{red}{290} x& = & 71 \\\Leftrightarrow & x = \frac{71}{290} & & \\ & V = \left\{ \frac{71}{290} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 24x-\frac{24}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-72} & = & \color{red}{165x} +44 \\\Leftrightarrow & 792x \color{red}{-72} \color{blue}{+72} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{+72} \\\Leftrightarrow & 792x-165x& = & 44+72 \\\Leftrightarrow & \color{red}{627} x& = & 116 \\\Leftrightarrow & x = \frac{116}{627} & & \\ & V = \left\{ \frac{116}{627} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{30}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+90} & = & \color{red}{105x} +14 \\\Leftrightarrow & 252x \color{red}{+90} \color{blue}{-90} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{-90} \\\Leftrightarrow & 252x-105x& = & 14-90 \\\Leftrightarrow & \color{red}{147} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{147} & & \\ & V = \left\{ \frac{-76}{147} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 6x+\frac{10}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+70} & = & \color{red}{385x} +22 \\\Leftrightarrow & 462x \color{red}{+70} \color{blue}{-70} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{-70} \\\Leftrightarrow & 462x-385x& = & 22-70 \\\Leftrightarrow & \color{red}{77} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{77} & & \\ & V = \left\{ \frac{-48}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{-30} & = & \color{red}{315x} +42 \\\Leftrightarrow & -140x \color{red}{-30} \color{blue}{+30} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+30} \\\Leftrightarrow & -140x-315x& = & 42+30 \\\Leftrightarrow & \color{red}{-455} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-455} & & \\\Leftrightarrow & x = \frac{-72}{455} & & \\ & V = \left\{ \frac{-72}{455} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{-108} & = & \color{red}{315x} +10 \\\Leftrightarrow & -405x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +10 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & -405x-315x& = & 10+108 \\\Leftrightarrow & \color{red}{-720} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-720} & & \\\Leftrightarrow & x = \frac{-59}{360} & & \\ & V = \left\{ \frac{-59}{360} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{11})& = & -5x+\frac{9}{5} \\\Leftrightarrow & 18x-\frac{24}{11}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-120} & = & \color{red}{-275x} +99 \\\Leftrightarrow & 990x \color{red}{-120} \color{blue}{+120} \color{blue}{+275x} & = & \color{red}{-275x} +99 \color{blue}{+275x} \color{blue}{+120} \\\Leftrightarrow & 990x+275x& = & 99+120 \\\Leftrightarrow & \color{red}{1265} x& = & 219 \\\Leftrightarrow & x = \frac{219}{1265} & & \\ & V = \left\{ \frac{219}{1265} \right\} & \\\end{align}\)