Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 24x-\frac{24}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{672}{ \color{blue}{28} }x- \frac{96}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 672x \color{red}{-96} & = & \color{red}{140x} +63 \\\Leftrightarrow & 672x \color{red}{-96} \color{blue}{+96} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{+96} \\\Leftrightarrow & 672x-140x& = & 63+96 \\\Leftrightarrow & \color{red}{532} x& = & 159 \\\Leftrightarrow & x = \frac{159}{532} & & \\ & V = \left\{ \frac{159}{532} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+18} & = & \color{red}{55x} +6 \\\Leftrightarrow & -132x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & -132x-55x& = & 6-18 \\\Leftrightarrow & \color{red}{-187} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-187} & & \\\Leftrightarrow & x = \frac{12}{187} & & \\ & V = \left\{ \frac{12}{187} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+4} & = & \color{red}{27x} +2 \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{-4} \\\Leftrightarrow & 24x-27x& = & 2-4 \\\Leftrightarrow & \color{red}{-3} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-3} & & \\\Leftrightarrow & x = \frac{2}{3} & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{9}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{99}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-99} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 462x \color{red}{-99} \color{blue}{+99} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{+99} \\\Leftrightarrow & 462x+385x& = & 14+99 \\\Leftrightarrow & \color{red}{847} x& = & 113 \\\Leftrightarrow & x = \frac{113}{847} & & \\ & V = \left\{ \frac{113}{847} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{7})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 8x-\frac{20}{7}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-20} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 56x \color{red}{-20} \color{blue}{+20} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+20} \\\Leftrightarrow & 56x+35x& = & 6+20 \\\Leftrightarrow & \color{red}{91} x& = & 26 \\\Leftrightarrow & x = \frac{26}{91} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{8})& = & -3x+\frac{5}{7} \\\Leftrightarrow & 28x-\frac{35}{8}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1568}{ \color{blue}{56} }x- \frac{245}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{40}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1568x \color{red}{-245} & = & \color{red}{-168x} +40 \\\Leftrightarrow & 1568x \color{red}{-245} \color{blue}{+245} \color{blue}{+168x} & = & \color{red}{-168x} +40 \color{blue}{+168x} \color{blue}{+245} \\\Leftrightarrow & 1568x+168x& = & 40+245 \\\Leftrightarrow & \color{red}{1736} x& = & 285 \\\Leftrightarrow & x = \frac{285}{1736} & & \\ & V = \left\{ \frac{285}{1736} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{3})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -6x+\frac{4}{3}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+44} & = & \color{red}{231x} +30 \\\Leftrightarrow & -198x \color{red}{+44} \color{blue}{-44} \color{blue}{-231x} & = & \color{red}{231x} +30 \color{blue}{-231x} \color{blue}{-44} \\\Leftrightarrow & -198x-231x& = & 30-44 \\\Leftrightarrow & \color{red}{-429} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-429} & & \\\Leftrightarrow & x = \frac{14}{429} & & \\ & V = \left\{ \frac{14}{429} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 18x-\frac{24}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1980}{ \color{blue}{110} }x- \frac{240}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1980x \color{red}{-240} & = & \color{red}{-550x} +99 \\\Leftrightarrow & 1980x \color{red}{-240} \color{blue}{+240} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{+240} \\\Leftrightarrow & 1980x+550x& = & 99+240 \\\Leftrightarrow & \color{red}{2530} x& = & 339 \\\Leftrightarrow & x = \frac{339}{2530} & & \\ & V = \left\{ \frac{339}{2530} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{-108} & = & \color{red}{225x} +40 \\\Leftrightarrow & -540x \color{red}{-108} \color{blue}{+108} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{+108} \\\Leftrightarrow & -540x-225x& = & 40+108 \\\Leftrightarrow & \color{red}{-765} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-765} & & \\\Leftrightarrow & x = \frac{-148}{765} & & \\ & V = \left\{ \frac{-148}{765} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 18x-\frac{24}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-168} & = & \color{red}{-175x} +30 \\\Leftrightarrow & 630x \color{red}{-168} \color{blue}{+168} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{+168} \\\Leftrightarrow & 630x+175x& = & 30+168 \\\Leftrightarrow & \color{red}{805} x& = & 198 \\\Leftrightarrow & x = \frac{198}{805} & & \\ & V = \left\{ \frac{198}{805} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{11})& = & -6x+\frac{3}{5} \\\Leftrightarrow & -18x+\frac{30}{11}& = & -6x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{-330}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+150} & = & \color{red}{-330x} +33 \\\Leftrightarrow & -990x \color{red}{+150} \color{blue}{-150} \color{blue}{+330x} & = & \color{red}{-330x} +33 \color{blue}{+330x} \color{blue}{-150} \\\Leftrightarrow & -990x+330x& = & 33-150 \\\Leftrightarrow & \color{red}{-660} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{-660} & & \\\Leftrightarrow & x = \frac{39}{220} & & \\ & V = \left\{ \frac{39}{220} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{7})& = & -3x+\frac{7}{3} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-30} & = & \color{red}{-63x} +49 \\\Leftrightarrow & 210x \color{red}{-30} \color{blue}{+30} \color{blue}{+63x} & = & \color{red}{-63x} +49 \color{blue}{+63x} \color{blue}{+30} \\\Leftrightarrow & 210x+63x& = & 49+30 \\\Leftrightarrow & \color{red}{273} x& = & 79 \\\Leftrightarrow & x = \frac{79}{273} & & \\ & V = \left\{ \frac{79}{273} \right\} & \\\end{align}\)