Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{4})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 14x-\frac{21}{4}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{616}{ \color{blue}{44} }x- \frac{231}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 616x \color{red}{-231} & = & \color{red}{220x} +12 \\\Leftrightarrow & 616x \color{red}{-231} \color{blue}{+231} \color{blue}{-220x} & = & \color{red}{220x} +12 \color{blue}{-220x} \color{blue}{+231} \\\Leftrightarrow & 616x-220x& = & 12+231 \\\Leftrightarrow & \color{red}{396} x& = & 243 \\\Leftrightarrow & x = \frac{243}{396} & & \\\Leftrightarrow & x = \frac{27}{44} & & \\ & V = \left\{ \frac{27}{44} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{6}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{50}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 50x \color{red}{+6} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 50x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & 50x+35x& = & 6-6 \\\Leftrightarrow & \color{red}{85} x& = & 0 \\\Leftrightarrow & x = \frac{0}{85} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{9})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 10x+\frac{4}{9}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+44} & = & \color{red}{693x} +18 \\\Leftrightarrow & 990x \color{red}{+44} \color{blue}{-44} \color{blue}{-693x} & = & \color{red}{693x} +18 \color{blue}{-693x} \color{blue}{-44} \\\Leftrightarrow & 990x-693x& = & 18-44 \\\Leftrightarrow & \color{red}{297} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{297} & & \\ & V = \left\{ \frac{-26}{297} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{4})& = & 6x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{25}{4}& = & 6x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-500}{ \color{blue}{20} }x- \frac{125}{ \color{blue}{20} })& = & (\frac{120}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -500x \color{red}{-125} & = & \color{red}{120x} +24 \\\Leftrightarrow & -500x \color{red}{-125} \color{blue}{+125} \color{blue}{-120x} & = & \color{red}{120x} +24 \color{blue}{-120x} \color{blue}{+125} \\\Leftrightarrow & -500x-120x& = & 24+125 \\\Leftrightarrow & \color{red}{-620} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-620} & & \\\Leftrightarrow & x = \frac{-149}{620} & & \\ & V = \left\{ \frac{-149}{620} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{3})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+100} & = & \color{red}{105x} +12 \\\Leftrightarrow & 150x \color{red}{+100} \color{blue}{-100} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{-100} \\\Leftrightarrow & 150x-105x& = & 12-100 \\\Leftrightarrow & \color{red}{45} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{45} & & \\ & V = \left\{ \frac{-88}{45} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{9})& = & -6x+\frac{4}{3} \\\Leftrightarrow & -28x+\frac{14}{9}& = & -6x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x+ \frac{14}{ \color{blue}{9} })& = & (\frac{-54}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{+14} & = & \color{red}{-54x} +12 \\\Leftrightarrow & -252x \color{red}{+14} \color{blue}{-14} \color{blue}{+54x} & = & \color{red}{-54x} +12 \color{blue}{+54x} \color{blue}{-14} \\\Leftrightarrow & -252x+54x& = & 12-14 \\\Leftrightarrow & \color{red}{-198} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-198} & & \\\Leftrightarrow & x = \frac{1}{99} & & \\ & V = \left\{ \frac{1}{99} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & 9x+\frac{5}{8} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x+ \frac{160}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{+160} & = & \color{red}{504x} +35 \\\Leftrightarrow & 1120x \color{red}{+160} \color{blue}{-160} \color{blue}{-504x} & = & \color{red}{504x} +35 \color{blue}{-504x} \color{blue}{-160} \\\Leftrightarrow & 1120x-504x& = & 35-160 \\\Leftrightarrow & \color{red}{616} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{616} & & \\ & V = \left\{ \frac{-125}{616} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+18} & = & \color{red}{-168x} +28 \\\Leftrightarrow & -315x \color{red}{+18} \color{blue}{-18} \color{blue}{+168x} & = & \color{red}{-168x} +28 \color{blue}{+168x} \color{blue}{-18} \\\Leftrightarrow & -315x+168x& = & 28-18 \\\Leftrightarrow & \color{red}{-147} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-147} & & \\\Leftrightarrow & x = \frac{-10}{147} & & \\ & V = \left\{ \frac{-10}{147} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{9})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -8x+\frac{10}{9}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-288}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -288x \color{red}{+40} & = & \color{red}{108x} +81 \\\Leftrightarrow & -288x \color{red}{+40} \color{blue}{-40} \color{blue}{-108x} & = & \color{red}{108x} +81 \color{blue}{-108x} \color{blue}{-40} \\\Leftrightarrow & -288x-108x& = & 81-40 \\\Leftrightarrow & \color{red}{-396} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-396} & & \\\Leftrightarrow & x = \frac{-41}{396} & & \\ & V = \left\{ \frac{-41}{396} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{10})& = & -4x+\frac{10}{9} \\\Leftrightarrow & 21x+\frac{21}{10}& = & -4x+\frac{10}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1890}{ \color{blue}{90} }x+ \frac{189}{ \color{blue}{90} })& = & (\frac{-360}{ \color{blue}{90} }x+ \frac{100}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1890x \color{red}{+189} & = & \color{red}{-360x} +100 \\\Leftrightarrow & 1890x \color{red}{+189} \color{blue}{-189} \color{blue}{+360x} & = & \color{red}{-360x} +100 \color{blue}{+360x} \color{blue}{-189} \\\Leftrightarrow & 1890x+360x& = & 100-189 \\\Leftrightarrow & \color{red}{2250} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{2250} & & \\ & V = \left\{ \frac{-89}{2250} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{11})& = & 9x+\frac{9}{7} \\\Leftrightarrow & 20x-\frac{8}{11}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{56}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-56} & = & \color{red}{693x} +99 \\\Leftrightarrow & 1540x \color{red}{-56} \color{blue}{+56} \color{blue}{-693x} & = & \color{red}{693x} +99 \color{blue}{-693x} \color{blue}{+56} \\\Leftrightarrow & 1540x-693x& = & 99+56 \\\Leftrightarrow & \color{red}{847} x& = & 155 \\\Leftrightarrow & x = \frac{155}{847} & & \\ & V = \left\{ \frac{155}{847} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{9})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{25}{9}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{25}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-25} & = & \color{red}{-27x} +12 \\\Leftrightarrow & -180x \color{red}{-25} \color{blue}{+25} \color{blue}{+27x} & = & \color{red}{-27x} +12 \color{blue}{+27x} \color{blue}{+25} \\\Leftrightarrow & -180x+27x& = & 12+25 \\\Leftrightarrow & \color{red}{-153} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-153} & & \\\Leftrightarrow & x = \frac{-37}{153} & & \\ & V = \left\{ \frac{-37}{153} \right\} & \\\end{align}\)