Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+88} & = & \color{red}{99x} +15 \\\Leftrightarrow & -264x \color{red}{+88} \color{blue}{-88} \color{blue}{-99x} & = & \color{red}{99x} +15 \color{blue}{-99x} \color{blue}{-88} \\\Leftrightarrow & -264x-99x& = & 15-88 \\\Leftrightarrow & \color{red}{-363} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-363} & & \\\Leftrightarrow & x = \frac{73}{363} & & \\ & V = \left\{ \frac{73}{363} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+72} & = & \color{red}{220x} +55 \\\Leftrightarrow & -528x \color{red}{+72} \color{blue}{-72} \color{blue}{-220x} & = & \color{red}{220x} +55 \color{blue}{-220x} \color{blue}{-72} \\\Leftrightarrow & -528x-220x& = & 55-72 \\\Leftrightarrow & \color{red}{-748} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-748} & & \\\Leftrightarrow & x = \frac{1}{44} & & \\ & V = \left\{ \frac{1}{44} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{5})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -20x+\frac{8}{5}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+88} & = & \color{red}{-385x} +25 \\\Leftrightarrow & -1100x \color{red}{+88} \color{blue}{-88} \color{blue}{+385x} & = & \color{red}{-385x} +25 \color{blue}{+385x} \color{blue}{-88} \\\Leftrightarrow & -1100x+385x& = & 25-88 \\\Leftrightarrow & \color{red}{-715} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-715} & & \\\Leftrightarrow & x = \frac{63}{715} & & \\ & V = \left\{ \frac{63}{715} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-90} & = & \color{red}{-275x} +66 \\\Leftrightarrow & -660x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & -660x+275x& = & 66+90 \\\Leftrightarrow & \color{red}{-385} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-385} & & \\\Leftrightarrow & x = \frac{-156}{385} & & \\ & V = \left\{ \frac{-156}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 12x+\frac{6}{5}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{720}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 720x \color{red}{+72} & = & \color{red}{420x} +25 \\\Leftrightarrow & 720x \color{red}{+72} \color{blue}{-72} \color{blue}{-420x} & = & \color{red}{420x} +25 \color{blue}{-420x} \color{blue}{-72} \\\Leftrightarrow & 720x-420x& = & 25-72 \\\Leftrightarrow & \color{red}{300} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{300} & & \\ & V = \left\{ \frac{-47}{300} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{11})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 10x+\frac{4}{11}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+28} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 770x \color{red}{+28} \color{blue}{-28} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{-28} \\\Leftrightarrow & 770x+231x& = & 22-28 \\\Leftrightarrow & \color{red}{1001} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{1001} & & \\ & V = \left\{ \frac{-6}{1001} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 6x+\frac{15}{4}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{264}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 264x \color{red}{+165} & = & \color{red}{220x} +8 \\\Leftrightarrow & 264x \color{red}{+165} \color{blue}{-165} \color{blue}{-220x} & = & \color{red}{220x} +8 \color{blue}{-220x} \color{blue}{-165} \\\Leftrightarrow & 264x-220x& = & 8-165 \\\Leftrightarrow & \color{red}{44} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{44} & & \\ & V = \left\{ \frac{-157}{44} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+132} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 1320x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 1320x+275x& = & 20-132 \\\Leftrightarrow & \color{red}{1595} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{1595} & & \\ & V = \left\{ \frac{-112}{1595} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & -6x+\frac{5}{2} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -6x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-60}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{+48} & = & \color{red}{-60x} +25 \\\Leftrightarrow & -180x \color{red}{+48} \color{blue}{-48} \color{blue}{+60x} & = & \color{red}{-60x} +25 \color{blue}{+60x} \color{blue}{-48} \\\Leftrightarrow & -180x+60x& = & 25-48 \\\Leftrightarrow & \color{red}{-120} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-120} & & \\\Leftrightarrow & x = \frac{23}{120} & & \\ & V = \left\{ \frac{23}{120} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-10} & = & \color{red}{-63x} +9 \\\Leftrightarrow & -28x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & -28x+63x& = & 9+10 \\\Leftrightarrow & \color{red}{35} x& = & 19 \\\Leftrightarrow & x = \frac{19}{35} & & \\ & V = \left\{ \frac{19}{35} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 15x+\frac{6}{5}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{+24} & = & \color{red}{-140x} +15 \\\Leftrightarrow & 300x \color{red}{+24} \color{blue}{-24} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{-24} \\\Leftrightarrow & 300x+140x& = & 15-24 \\\Leftrightarrow & \color{red}{440} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{440} & & \\ & V = \left\{ \frac{-9}{440} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 18x+\frac{30}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{+60} & = & \color{red}{-98x} +35 \\\Leftrightarrow & 252x \color{red}{+60} \color{blue}{-60} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{-60} \\\Leftrightarrow & 252x+98x& = & 35-60 \\\Leftrightarrow & \color{red}{350} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{350} & & \\\Leftrightarrow & x = \frac{-1}{14} & & \\ & V = \left\{ \frac{-1}{14} \right\} & \\\end{align}\)