Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{-30} & = & \color{red}{35x} +9 \\\Leftrightarrow & 168x \color{red}{-30} \color{blue}{+30} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{+30} \\\Leftrightarrow & 168x-35x& = & 9+30 \\\Leftrightarrow & \color{red}{133} x& = & 39 \\\Leftrightarrow & x = \frac{39}{133} & & \\ & V = \left\{ \frac{39}{133} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & 3x+\frac{3}{7} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+10} & = & \color{red}{21x} +3 \\\Leftrightarrow & 28x \color{red}{+10} \color{blue}{-10} \color{blue}{-21x} & = & \color{red}{21x} +3 \color{blue}{-21x} \color{blue}{-10} \\\Leftrightarrow & 28x-21x& = & 3-10 \\\Leftrightarrow & \color{red}{7} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{7} & & \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 12x+\frac{6}{5}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{+24} & = & \color{red}{100x} +25 \\\Leftrightarrow & 240x \color{red}{+24} \color{blue}{-24} \color{blue}{-100x} & = & \color{red}{100x} +25 \color{blue}{-100x} \color{blue}{-24} \\\Leftrightarrow & 240x-100x& = & 25-24 \\\Leftrightarrow & \color{red}{140} x& = & 1 \\\Leftrightarrow & x = \frac{1}{140} & & \\ & V = \left\{ \frac{1}{140} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{7})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-220} & = & \color{red}{-539x} +21 \\\Leftrightarrow & -1232x \color{red}{-220} \color{blue}{+220} \color{blue}{+539x} & = & \color{red}{-539x} +21 \color{blue}{+539x} \color{blue}{+220} \\\Leftrightarrow & -1232x+539x& = & 21+220 \\\Leftrightarrow & \color{red}{-693} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-693} & & \\\Leftrightarrow & x = \frac{-241}{693} & & \\ & V = \left\{ \frac{-241}{693} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{7})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 8x-\frac{4}{7}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{44}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-44} & = & \color{red}{231x} +14 \\\Leftrightarrow & 616x \color{red}{-44} \color{blue}{+44} \color{blue}{-231x} & = & \color{red}{231x} +14 \color{blue}{-231x} \color{blue}{+44} \\\Leftrightarrow & 616x-231x& = & 14+44 \\\Leftrightarrow & \color{red}{385} x& = & 58 \\\Leftrightarrow & x = \frac{58}{385} & & \\ & V = \left\{ \frac{58}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & -5x+\frac{5}{9} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{-108} & = & \color{red}{-225x} +25 \\\Leftrightarrow & -540x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +25 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & -540x+225x& = & 25+108 \\\Leftrightarrow & \color{red}{-315} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-315} & & \\\Leftrightarrow & x = \frac{-19}{45} & & \\ & V = \left\{ \frac{-19}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{11})& = & 4x+\frac{2}{9} \\\Leftrightarrow & 21x+\frac{35}{11}& = & 4x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x+ \frac{315}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{+315} & = & \color{red}{396x} +22 \\\Leftrightarrow & 2079x \color{red}{+315} \color{blue}{-315} \color{blue}{-396x} & = & \color{red}{396x} +22 \color{blue}{-396x} \color{blue}{-315} \\\Leftrightarrow & 2079x-396x& = & 22-315 \\\Leftrightarrow & \color{red}{1683} x& = & -293 \\\Leftrightarrow & x = \frac{-293}{1683} & & \\ & V = \left\{ \frac{-293}{1683} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{11})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 24x-\frac{12}{11}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{-108} & = & \color{red}{495x} +22 \\\Leftrightarrow & 2376x \color{red}{-108} \color{blue}{+108} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{+108} \\\Leftrightarrow & 2376x-495x& = & 22+108 \\\Leftrightarrow & \color{red}{1881} x& = & 130 \\\Leftrightarrow & x = \frac{130}{1881} & & \\ & V = \left\{ \frac{130}{1881} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{9})& = & -9x+\frac{3}{7} \\\Leftrightarrow & 4x-\frac{4}{9}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{-28} & = & \color{red}{-567x} +27 \\\Leftrightarrow & 252x \color{red}{-28} \color{blue}{+28} \color{blue}{+567x} & = & \color{red}{-567x} +27 \color{blue}{+567x} \color{blue}{+28} \\\Leftrightarrow & 252x+567x& = & 27+28 \\\Leftrightarrow & \color{red}{819} x& = & 55 \\\Leftrightarrow & x = \frac{55}{819} & & \\ & V = \left\{ \frac{55}{819} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{11})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 20x+\frac{16}{11}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{144}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+144} & = & \color{red}{-297x} +88 \\\Leftrightarrow & 1980x \color{red}{+144} \color{blue}{-144} \color{blue}{+297x} & = & \color{red}{-297x} +88 \color{blue}{+297x} \color{blue}{-144} \\\Leftrightarrow & 1980x+297x& = & 88-144 \\\Leftrightarrow & \color{red}{2277} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{2277} & & \\ & V = \left\{ \frac{-56}{2277} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x+\frac{30}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+150} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1650x \color{red}{+150} \color{blue}{-150} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-150} \\\Leftrightarrow & -1650x+385x& = & 66-150 \\\Leftrightarrow & \color{red}{-1265} x& = & -84 \\\Leftrightarrow & x = \frac{-84}{-1265} & & \\\Leftrightarrow & x = \frac{84}{1265} & & \\ & V = \left\{ \frac{84}{1265} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & -7x+\frac{8}{5} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{-140x} +32 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +32 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & 300x+140x& = & 32+75 \\\Leftrightarrow & \color{red}{440} x& = & 107 \\\Leftrightarrow & x = \frac{107}{440} & & \\ & V = \left\{ \frac{107}{440} \right\} & \\\end{align}\)