Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+6} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -42x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & -42x+49x& = & 10-6 \\\Leftrightarrow & \color{red}{7} x& = & 4 \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{11})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 24x-\frac{24}{11}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{-216} & = & \color{red}{-495x} +77 \\\Leftrightarrow & 2376x \color{red}{-216} \color{blue}{+216} \color{blue}{+495x} & = & \color{red}{-495x} +77 \color{blue}{+495x} \color{blue}{+216} \\\Leftrightarrow & 2376x+495x& = & 77+216 \\\Leftrightarrow & \color{red}{2871} x& = & 293 \\\Leftrightarrow & x = \frac{293}{2871} & & \\ & V = \left\{ \frac{293}{2871} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-40} & = & \color{red}{98x} +21 \\\Leftrightarrow & 280x \color{red}{-40} \color{blue}{+40} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{+40} \\\Leftrightarrow & 280x-98x& = & 21+40 \\\Leftrightarrow & \color{red}{182} x& = & 61 \\\Leftrightarrow & x = \frac{61}{182} & & \\ & V = \left\{ \frac{61}{182} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -12x+\frac{16}{7}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x+ \frac{160}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{+160} & = & \color{red}{-350x} +21 \\\Leftrightarrow & -840x \color{red}{+160} \color{blue}{-160} \color{blue}{+350x} & = & \color{red}{-350x} +21 \color{blue}{+350x} \color{blue}{-160} \\\Leftrightarrow & -840x+350x& = & 21-160 \\\Leftrightarrow & \color{red}{-490} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-490} & & \\\Leftrightarrow & x = \frac{139}{490} & & \\ & V = \left\{ \frac{139}{490} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{6}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-24} & = & \color{red}{140x} +63 \\\Leftrightarrow & -336x \color{red}{-24} \color{blue}{+24} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{+24} \\\Leftrightarrow & -336x-140x& = & 63+24 \\\Leftrightarrow & \color{red}{-476} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-476} & & \\\Leftrightarrow & x = \frac{-87}{476} & & \\ & V = \left\{ \frac{-87}{476} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{4})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -6x-\frac{9}{4}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x- \frac{27}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{-27} & = & \color{red}{-84x} +10 \\\Leftrightarrow & -72x \color{red}{-27} \color{blue}{+27} \color{blue}{+84x} & = & \color{red}{-84x} +10 \color{blue}{+84x} \color{blue}{+27} \\\Leftrightarrow & -72x+84x& = & 10+27 \\\Leftrightarrow & \color{red}{12} x& = & 37 \\\Leftrightarrow & x = \frac{37}{12} & & \\ & V = \left\{ \frac{37}{12} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{4})& = & 9x+\frac{2}{5} \\\Leftrightarrow & 28x-\frac{21}{4}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{560}{ \color{blue}{20} }x- \frac{105}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{8}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 560x \color{red}{-105} & = & \color{red}{180x} +8 \\\Leftrightarrow & 560x \color{red}{-105} \color{blue}{+105} \color{blue}{-180x} & = & \color{red}{180x} +8 \color{blue}{-180x} \color{blue}{+105} \\\Leftrightarrow & 560x-180x& = & 8+105 \\\Leftrightarrow & \color{red}{380} x& = & 113 \\\Leftrightarrow & x = \frac{113}{380} & & \\ & V = \left\{ \frac{113}{380} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x+\frac{6}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+66} & = & \color{red}{-275x} +50 \\\Leftrightarrow & 660x \color{red}{+66} \color{blue}{-66} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{-66} \\\Leftrightarrow & 660x+275x& = & 50-66 \\\Leftrightarrow & \color{red}{935} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{935} & & \\ & V = \left\{ \frac{-16}{935} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{11})& = & -3x+\frac{5}{3} \\\Leftrightarrow & -20x-\frac{16}{11}& = & -3x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-48} & = & \color{red}{-99x} +55 \\\Leftrightarrow & -660x \color{red}{-48} \color{blue}{+48} \color{blue}{+99x} & = & \color{red}{-99x} +55 \color{blue}{+99x} \color{blue}{+48} \\\Leftrightarrow & -660x+99x& = & 55+48 \\\Leftrightarrow & \color{red}{-561} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-561} & & \\\Leftrightarrow & x = \frac{-103}{561} & & \\ & V = \left\{ \frac{-103}{561} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{5})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 10x+\frac{4}{5}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+28} & = & \color{red}{105x} +30 \\\Leftrightarrow & 350x \color{red}{+28} \color{blue}{-28} \color{blue}{-105x} & = & \color{red}{105x} +30 \color{blue}{-105x} \color{blue}{-28} \\\Leftrightarrow & 350x-105x& = & 30-28 \\\Leftrightarrow & \color{red}{245} x& = & 2 \\\Leftrightarrow & x = \frac{2}{245} & & \\ & V = \left\{ \frac{2}{245} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{12})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{25}{12}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+25} & = & \color{red}{-84x} +8 \\\Leftrightarrow & -120x \color{red}{+25} \color{blue}{-25} \color{blue}{+84x} & = & \color{red}{-84x} +8 \color{blue}{+84x} \color{blue}{-25} \\\Leftrightarrow & -120x+84x& = & 8-25 \\\Leftrightarrow & \color{red}{-36} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-36} & & \\\Leftrightarrow & x = \frac{17}{36} & & \\ & V = \left\{ \frac{17}{36} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-2100}{ \color{blue}{70} }x+ \frac{300}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -2100x \color{red}{+300} & = & \color{red}{-490x} +49 \\\Leftrightarrow & -2100x \color{red}{+300} \color{blue}{-300} \color{blue}{+490x} & = & \color{red}{-490x} +49 \color{blue}{+490x} \color{blue}{-300} \\\Leftrightarrow & -2100x+490x& = & 49-300 \\\Leftrightarrow & \color{red}{-1610} x& = & -251 \\\Leftrightarrow & x = \frac{-251}{-1610} & & \\\Leftrightarrow & x = \frac{251}{1610} & & \\ & V = \left\{ \frac{251}{1610} \right\} & \\\end{align}\)