Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{3})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{+14} & = & \color{red}{24x} +10 \\\Leftrightarrow & -63x \color{red}{+14} \color{blue}{-14} \color{blue}{-24x} & = & \color{red}{24x} +10 \color{blue}{-24x} \color{blue}{-14} \\\Leftrightarrow & -63x-24x& = & 10-14 \\\Leftrightarrow & \color{red}{-87} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-87} & & \\\Leftrightarrow & x = \frac{4}{87} & & \\ & V = \left\{ \frac{4}{87} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{15}{4}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-105} & = & \color{red}{-140x} +40 \\\Leftrightarrow & -336x \color{red}{-105} \color{blue}{+105} \color{blue}{+140x} & = & \color{red}{-140x} +40 \color{blue}{+140x} \color{blue}{+105} \\\Leftrightarrow & -336x+140x& = & 40+105 \\\Leftrightarrow & \color{red}{-196} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-196} & & \\\Leftrightarrow & x = \frac{-145}{196} & & \\ & V = \left\{ \frac{-145}{196} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{7})& = & 6x+\frac{10}{11} \\\Leftrightarrow & 25x-\frac{10}{7}& = & 6x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{462}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-110} & = & \color{red}{462x} +70 \\\Leftrightarrow & 1925x \color{red}{-110} \color{blue}{+110} \color{blue}{-462x} & = & \color{red}{462x} +70 \color{blue}{-462x} \color{blue}{+110} \\\Leftrightarrow & 1925x-462x& = & 70+110 \\\Leftrightarrow & \color{red}{1463} x& = & 180 \\\Leftrightarrow & x = \frac{180}{1463} & & \\ & V = \left\{ \frac{180}{1463} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{5})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{+48} & = & \color{red}{-70x} +3 \\\Leftrightarrow & 300x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & 300x+70x& = & 3-48 \\\Leftrightarrow & \color{red}{370} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{370} & & \\\Leftrightarrow & x = \frac{-9}{74} & & \\ & V = \left\{ \frac{-9}{74} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{12}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+12} & = & \color{red}{55x} +2 \\\Leftrightarrow & -132x \color{red}{+12} \color{blue}{-12} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{-12} \\\Leftrightarrow & -132x-55x& = & 2-12 \\\Leftrightarrow & \color{red}{-187} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-187} & & \\\Leftrightarrow & x = \frac{10}{187} & & \\ & V = \left\{ \frac{10}{187} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+48} & = & \color{red}{-70x} +45 \\\Leftrightarrow & -300x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & -300x+70x& = & 45-48 \\\Leftrightarrow & \color{red}{-230} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-230} & & \\\Leftrightarrow & x = \frac{3}{230} & & \\ & V = \left\{ \frac{3}{230} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 18x-\frac{30}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-210} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 1386x \color{red}{-210} \color{blue}{+210} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{+210} \\\Leftrightarrow & 1386x+385x& = & 110+210 \\\Leftrightarrow & \color{red}{1771} x& = & 320 \\\Leftrightarrow & x = \frac{320}{1771} & & \\ & V = \left\{ \frac{320}{1771} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{4}{5}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{-8} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 100x \color{red}{-8} \color{blue}{+8} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{+8} \\\Leftrightarrow & 100x+70x& = & 35+8 \\\Leftrightarrow & \color{red}{170} x& = & 43 \\\Leftrightarrow & x = \frac{43}{170} & & \\ & V = \left\{ \frac{43}{170} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{3})& = & 4x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{10}{3}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{+110} & = & \color{red}{132x} +30 \\\Leftrightarrow & -495x \color{red}{+110} \color{blue}{-110} \color{blue}{-132x} & = & \color{red}{132x} +30 \color{blue}{-132x} \color{blue}{-110} \\\Leftrightarrow & -495x-132x& = & 30-110 \\\Leftrightarrow & \color{red}{-627} x& = & -80 \\\Leftrightarrow & x = \frac{-80}{-627} & & \\\Leftrightarrow & x = \frac{80}{627} & & \\ & V = \left\{ \frac{80}{627} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{11})& = & 9x+\frac{2}{11} \\\Leftrightarrow & -4x-\frac{8}{11}& = & 9x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{-8} & = & \color{red}{99x} +2 \\\Leftrightarrow & -44x \color{red}{-8} \color{blue}{+8} \color{blue}{-99x} & = & \color{red}{99x} +2 \color{blue}{-99x} \color{blue}{+8} \\\Leftrightarrow & -44x-99x& = & 2+8 \\\Leftrightarrow & \color{red}{-143} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-143} & & \\\Leftrightarrow & x = \frac{-10}{143} & & \\ & V = \left\{ \frac{-10}{143} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -20x-\frac{8}{9}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{21}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-8} & = & \color{red}{-63x} +21 \\\Leftrightarrow & -180x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +21 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -180x+63x& = & 21+8 \\\Leftrightarrow & \color{red}{-117} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-117} & & \\\Leftrightarrow & x = \frac{-29}{117} & & \\ & V = \left\{ \frac{-29}{117} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-99} & = & \color{red}{275x} +30 \\\Leftrightarrow & 330x \color{red}{-99} \color{blue}{+99} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{+99} \\\Leftrightarrow & 330x-275x& = & 30+99 \\\Leftrightarrow & \color{red}{55} x& = & 129 \\\Leftrightarrow & x = \frac{129}{55} & & \\ & V = \left\{ \frac{129}{55} \right\} & \\\end{align}\)