Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -10x-\frac{20}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-700}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -700x \color{red}{-200} & = & \color{red}{490x} +63 \\\Leftrightarrow & -700x \color{red}{-200} \color{blue}{+200} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+200} \\\Leftrightarrow & -700x-490x& = & 63+200 \\\Leftrightarrow & \color{red}{-1190} x& = & 263 \\\Leftrightarrow & x = \frac{263}{-1190} & & \\\Leftrightarrow & x = \frac{-263}{1190} & & \\ & V = \left\{ \frac{-263}{1190} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{2})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{15}{2}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-108}{ \color{blue}{18} }x+ \frac{135}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -108x \color{red}{+135} & = & \color{red}{-126x} +20 \\\Leftrightarrow & -108x \color{red}{+135} \color{blue}{-135} \color{blue}{+126x} & = & \color{red}{-126x} +20 \color{blue}{+126x} \color{blue}{-135} \\\Leftrightarrow & -108x+126x& = & 20-135 \\\Leftrightarrow & \color{red}{18} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{18} & & \\ & V = \left\{ \frac{-115}{18} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{11})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x+\frac{8}{11}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+8} & = & \color{red}{55x} +4 \\\Leftrightarrow & -132x \color{red}{+8} \color{blue}{-8} \color{blue}{-55x} & = & \color{red}{55x} +4 \color{blue}{-55x} \color{blue}{-8} \\\Leftrightarrow & -132x-55x& = & 4-8 \\\Leftrightarrow & \color{red}{-187} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-187} & & \\\Leftrightarrow & x = \frac{4}{187} & & \\ & V = \left\{ \frac{4}{187} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{6})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -14x-\frac{35}{6}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-252}{ \color{blue}{18} }x- \frac{105}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -252x \color{red}{-105} & = & \color{red}{54x} +16 \\\Leftrightarrow & -252x \color{red}{-105} \color{blue}{+105} \color{blue}{-54x} & = & \color{red}{54x} +16 \color{blue}{-54x} \color{blue}{+105} \\\Leftrightarrow & -252x-54x& = & 16+105 \\\Leftrightarrow & \color{red}{-306} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-306} & & \\\Leftrightarrow & x = \frac{-121}{306} & & \\ & V = \left\{ \frac{-121}{306} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{11})& = & -3x+\frac{9}{7} \\\Leftrightarrow & -8x+\frac{6}{11}& = & -3x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+42} & = & \color{red}{-231x} +99 \\\Leftrightarrow & -616x \color{red}{+42} \color{blue}{-42} \color{blue}{+231x} & = & \color{red}{-231x} +99 \color{blue}{+231x} \color{blue}{-42} \\\Leftrightarrow & -616x+231x& = & 99-42 \\\Leftrightarrow & \color{red}{-385} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-385} & & \\\Leftrightarrow & x = \frac{-57}{385} & & \\ & V = \left\{ \frac{-57}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{147x} +70 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+60} \\\Leftrightarrow & 420x-147x& = & 70+60 \\\Leftrightarrow & \color{red}{273} x& = & 130 \\\Leftrightarrow & x = \frac{130}{273} & & \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{11})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+42} & = & \color{red}{-539x} +44 \\\Leftrightarrow & 462x \color{red}{+42} \color{blue}{-42} \color{blue}{+539x} & = & \color{red}{-539x} +44 \color{blue}{+539x} \color{blue}{-42} \\\Leftrightarrow & 462x+539x& = & 44-42 \\\Leftrightarrow & \color{red}{1001} x& = & 2 \\\Leftrightarrow & x = \frac{2}{1001} & & \\ & V = \left\{ \frac{2}{1001} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{7})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 8x+\frac{10}{7}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{-189x} +28 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{-30} \\\Leftrightarrow & 168x+189x& = & 28-30 \\\Leftrightarrow & \color{red}{357} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{357} & & \\ & V = \left\{ \frac{-2}{357} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-60} & = & \color{red}{-110x} +99 \\\Leftrightarrow & -264x \color{red}{-60} \color{blue}{+60} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+60} \\\Leftrightarrow & -264x+110x& = & 99+60 \\\Leftrightarrow & \color{red}{-154} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-154} & & \\\Leftrightarrow & x = \frac{-159}{154} & & \\ & V = \left\{ \frac{-159}{154} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{20}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+180} & = & \color{red}{-315x} +56 \\\Leftrightarrow & 756x \color{red}{+180} \color{blue}{-180} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{-180} \\\Leftrightarrow & 756x+315x& = & 56-180 \\\Leftrightarrow & \color{red}{1071} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{1071} & & \\ & V = \left\{ \frac{-124}{1071} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-18} & = & \color{red}{63x} +28 \\\Leftrightarrow & -168x \color{red}{-18} \color{blue}{+18} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{+18} \\\Leftrightarrow & -168x-63x& = & 28+18 \\\Leftrightarrow & \color{red}{-231} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-231} & & \\\Leftrightarrow & x = \frac{-46}{231} & & \\ & V = \left\{ \frac{-46}{231} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+90} & = & \color{red}{-441x} +28 \\\Leftrightarrow & -378x \color{red}{+90} \color{blue}{-90} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{-90} \\\Leftrightarrow & -378x+441x& = & 28-90 \\\Leftrightarrow & \color{red}{63} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{63} & & \\ & V = \left\{ \frac{-62}{63} \right\} & \\\end{align}\)