Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{5}{9} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{5}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{40}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{-189} & = & \color{red}{-216x} +40 \\\Leftrightarrow & -1008x \color{red}{-189} \color{blue}{+189} \color{blue}{+216x} & = & \color{red}{-216x} +40 \color{blue}{+216x} \color{blue}{+189} \\\Leftrightarrow & -1008x+216x& = & 40+189 \\\Leftrightarrow & \color{red}{-792} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-792} & & \\\Leftrightarrow & x = \frac{-229}{792} & & \\ & V = \left\{ \frac{-229}{792} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & -5x+\frac{5}{4} \\\Leftrightarrow & -12x+\frac{24}{11}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+96} & = & \color{red}{-220x} +55 \\\Leftrightarrow & -528x \color{red}{+96} \color{blue}{-96} \color{blue}{+220x} & = & \color{red}{-220x} +55 \color{blue}{+220x} \color{blue}{-96} \\\Leftrightarrow & -528x+220x& = & 55-96 \\\Leftrightarrow & \color{red}{-308} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-308} & & \\\Leftrightarrow & x = \frac{41}{308} & & \\ & V = \left\{ \frac{41}{308} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{10})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{9}{10}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-540}{ \color{blue}{90} }x- \frac{81}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{40}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -540x \color{red}{-81} & = & \color{red}{-630x} +40 \\\Leftrightarrow & -540x \color{red}{-81} \color{blue}{+81} \color{blue}{+630x} & = & \color{red}{-630x} +40 \color{blue}{+630x} \color{blue}{+81} \\\Leftrightarrow & -540x+630x& = & 40+81 \\\Leftrightarrow & \color{red}{90} x& = & 121 \\\Leftrightarrow & x = \frac{121}{90} & & \\ & V = \left\{ \frac{121}{90} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{4}{9})& = & -8x+\frac{5}{6} \\\Leftrightarrow & 21x+\frac{28}{9}& = & -8x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{378}{ \color{blue}{18} }x+ \frac{56}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 378x \color{red}{+56} & = & \color{red}{-144x} +15 \\\Leftrightarrow & 378x \color{red}{+56} \color{blue}{-56} \color{blue}{+144x} & = & \color{red}{-144x} +15 \color{blue}{+144x} \color{blue}{-56} \\\Leftrightarrow & 378x+144x& = & 15-56 \\\Leftrightarrow & \color{red}{522} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{522} & & \\ & V = \left\{ \frac{-41}{522} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 6x+\frac{4}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{+16} & = & \color{red}{140x} +63 \\\Leftrightarrow & 168x \color{red}{+16} \color{blue}{-16} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{-16} \\\Leftrightarrow & 168x-140x& = & 63-16 \\\Leftrightarrow & \color{red}{28} x& = & 47 \\\Leftrightarrow & x = \frac{47}{28} & & \\ & V = \left\{ \frac{47}{28} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{275x} +25 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 660x-275x& = & 25+132 \\\Leftrightarrow & \color{red}{385} x& = & 157 \\\Leftrightarrow & x = \frac{157}{385} & & \\ & V = \left\{ \frac{157}{385} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{7})& = & 2x+\frac{8}{11} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-110} & = & \color{red}{154x} +56 \\\Leftrightarrow & 1155x \color{red}{-110} \color{blue}{+110} \color{blue}{-154x} & = & \color{red}{154x} +56 \color{blue}{-154x} \color{blue}{+110} \\\Leftrightarrow & 1155x-154x& = & 56+110 \\\Leftrightarrow & \color{red}{1001} x& = & 166 \\\Leftrightarrow & x = \frac{166}{1001} & & \\ & V = \left\{ \frac{166}{1001} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 8x-\frac{4}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x- \frac{16}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{-16} & = & \color{red}{196x} +21 \\\Leftrightarrow & 224x \color{red}{-16} \color{blue}{+16} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{+16} \\\Leftrightarrow & 224x-196x& = & 21+16 \\\Leftrightarrow & \color{red}{28} x& = & 37 \\\Leftrightarrow & x = \frac{37}{28} & & \\ & V = \left\{ \frac{37}{28} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+30} & = & \color{red}{-105x} +70 \\\Leftrightarrow & 84x \color{red}{+30} \color{blue}{-30} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-30} \\\Leftrightarrow & 84x+105x& = & 70-30 \\\Leftrightarrow & \color{red}{189} x& = & 40 \\\Leftrightarrow & x = \frac{40}{189} & & \\ & V = \left\{ \frac{40}{189} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -30x+\frac{18}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+54} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -450x \color{red}{+54} \color{blue}{-54} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{-54} \\\Leftrightarrow & -450x+105x& = & 20-54 \\\Leftrightarrow & \color{red}{-345} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-345} & & \\\Leftrightarrow & x = \frac{34}{345} & & \\ & V = \left\{ \frac{34}{345} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{2})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 12x-\frac{9}{2}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-63} & = & \color{red}{-70x} +4 \\\Leftrightarrow & 168x \color{red}{-63} \color{blue}{+63} \color{blue}{+70x} & = & \color{red}{-70x} +4 \color{blue}{+70x} \color{blue}{+63} \\\Leftrightarrow & 168x+70x& = & 4+63 \\\Leftrightarrow & \color{red}{238} x& = & 67 \\\Leftrightarrow & x = \frac{67}{238} & & \\ & V = \left\{ \frac{67}{238} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{5})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -16x+\frac{8}{5}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{+8} & = & \color{red}{35x} +2 \\\Leftrightarrow & -80x \color{red}{+8} \color{blue}{-8} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-8} \\\Leftrightarrow & -80x-35x& = & 2-8 \\\Leftrightarrow & \color{red}{-115} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-115} & & \\\Leftrightarrow & x = \frac{6}{115} & & \\ & V = \left\{ \frac{6}{115} \right\} & \\\end{align}\)