Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{9})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{28}{9}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1575}{ \color{blue}{45} }x- \frac{140}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1575x \color{red}{-140} & = & \color{red}{360x} +54 \\\Leftrightarrow & 1575x \color{red}{-140} \color{blue}{+140} \color{blue}{-360x} & = & \color{red}{360x} +54 \color{blue}{-360x} \color{blue}{+140} \\\Leftrightarrow & 1575x-360x& = & 54+140 \\\Leftrightarrow & \color{red}{1215} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1215} & & \\ & V = \left\{ \frac{194}{1215} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{2})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -35x+\frac{21}{2}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-770}{ \color{blue}{22} }x+ \frac{231}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -770x \color{red}{+231} & = & \color{red}{-66x} +8 \\\Leftrightarrow & -770x \color{red}{+231} \color{blue}{-231} \color{blue}{+66x} & = & \color{red}{-66x} +8 \color{blue}{+66x} \color{blue}{-231} \\\Leftrightarrow & -770x+66x& = & 8-231 \\\Leftrightarrow & \color{red}{-704} x& = & -223 \\\Leftrightarrow & x = \frac{-223}{-704} & & \\\Leftrightarrow & x = \frac{223}{704} & & \\ & V = \left\{ \frac{223}{704} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{11})& = & 8x+\frac{5}{11} \\\Leftrightarrow & -15x-\frac{10}{11}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-10} & = & \color{red}{88x} +5 \\\Leftrightarrow & -165x \color{red}{-10} \color{blue}{+10} \color{blue}{-88x} & = & \color{red}{88x} +5 \color{blue}{-88x} \color{blue}{+10} \\\Leftrightarrow & -165x-88x& = & 5+10 \\\Leftrightarrow & \color{red}{-253} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-253} & & \\\Leftrightarrow & x = \frac{-15}{253} & & \\ & V = \left\{ \frac{-15}{253} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -16x+\frac{16}{7}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{+176} & = & \color{red}{539x} +28 \\\Leftrightarrow & -1232x \color{red}{+176} \color{blue}{-176} \color{blue}{-539x} & = & \color{red}{539x} +28 \color{blue}{-539x} \color{blue}{-176} \\\Leftrightarrow & -1232x-539x& = & 28-176 \\\Leftrightarrow & \color{red}{-1771} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{-1771} & & \\\Leftrightarrow & x = \frac{148}{1771} & & \\ & V = \left\{ \frac{148}{1771} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{7})& = & 8x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{15}{7}& = & 8x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{30}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{112x} +21 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{-112x} & = & \color{red}{112x} +21 \color{blue}{-112x} \color{blue}{+30} \\\Leftrightarrow & -210x-112x& = & 21+30 \\\Leftrightarrow & \color{red}{-322} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-322} & & \\\Leftrightarrow & x = \frac{-51}{322} & & \\ & V = \left\{ \frac{-51}{322} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{-12} & = & \color{red}{-42x} +35 \\\Leftrightarrow & -112x \color{red}{-12} \color{blue}{+12} \color{blue}{+42x} & = & \color{red}{-42x} +35 \color{blue}{+42x} \color{blue}{+12} \\\Leftrightarrow & -112x+42x& = & 35+12 \\\Leftrightarrow & \color{red}{-70} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-70} & & \\\Leftrightarrow & x = \frac{-47}{70} & & \\ & V = \left\{ \frac{-47}{70} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{11})& = & -4x+\frac{4}{9} \\\Leftrightarrow & -15x-\frac{6}{11}& = & -4x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{-396}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{-54} & = & \color{red}{-396x} +44 \\\Leftrightarrow & -1485x \color{red}{-54} \color{blue}{+54} \color{blue}{+396x} & = & \color{red}{-396x} +44 \color{blue}{+396x} \color{blue}{+54} \\\Leftrightarrow & -1485x+396x& = & 44+54 \\\Leftrightarrow & \color{red}{-1089} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-1089} & & \\\Leftrightarrow & x = \frac{-98}{1089} & & \\ & V = \left\{ \frac{-98}{1089} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-8} & = & \color{red}{-81x} +30 \\\Leftrightarrow & -72x \color{red}{-8} \color{blue}{+8} \color{blue}{+81x} & = & \color{red}{-81x} +30 \color{blue}{+81x} \color{blue}{+8} \\\Leftrightarrow & -72x+81x& = & 30+8 \\\Leftrightarrow & \color{red}{9} x& = & 38 \\\Leftrightarrow & x = \frac{38}{9} & & \\ & V = \left\{ \frac{38}{9} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 8x+\frac{3}{10} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 8x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x- \frac{140}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{-140} & = & \color{red}{240x} +9 \\\Leftrightarrow & 1050x \color{red}{-140} \color{blue}{+140} \color{blue}{-240x} & = & \color{red}{240x} +9 \color{blue}{-240x} \color{blue}{+140} \\\Leftrightarrow & 1050x-240x& = & 9+140 \\\Leftrightarrow & \color{red}{810} x& = & 149 \\\Leftrightarrow & x = \frac{149}{810} & & \\ & V = \left\{ \frac{149}{810} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & -180x+75x& = & 40+36 \\\Leftrightarrow & \color{red}{-105} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-105} & & \\\Leftrightarrow & x = \frac{-76}{105} & & \\ & V = \left\{ \frac{-76}{105} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-132} & = & \color{red}{385x} +10 \\\Leftrightarrow & 1650x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & 1650x-385x& = & 10+132 \\\Leftrightarrow & \color{red}{1265} x& = & 142 \\\Leftrightarrow & x = \frac{142}{1265} & & \\ & V = \left\{ \frac{142}{1265} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{2})& = & 8x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{25}{2}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{175}{ \color{blue}{14} })& = & (\frac{112}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+175} & = & \color{red}{112x} +20 \\\Leftrightarrow & 210x \color{red}{+175} \color{blue}{-175} \color{blue}{-112x} & = & \color{red}{112x} +20 \color{blue}{-112x} \color{blue}{-175} \\\Leftrightarrow & 210x-112x& = & 20-175 \\\Leftrightarrow & \color{red}{98} x& = & -155 \\\Leftrightarrow & x = \frac{-155}{98} & & \\ & V = \left\{ \frac{-155}{98} \right\} & \\\end{align}\)