Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+84} & = & \color{red}{-175x} +30 \\\Leftrightarrow & -840x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & -840x+175x& = & 30-84 \\\Leftrightarrow & \color{red}{-665} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-665} & & \\\Leftrightarrow & x = \frac{54}{665} & & \\ & V = \left\{ \frac{54}{665} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 28x+\frac{28}{9}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2016}{ \color{blue}{72} }x+ \frac{224}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2016x \color{red}{+224} & = & \color{red}{-360x} +27 \\\Leftrightarrow & 2016x \color{red}{+224} \color{blue}{-224} \color{blue}{+360x} & = & \color{red}{-360x} +27 \color{blue}{+360x} \color{blue}{-224} \\\Leftrightarrow & 2016x+360x& = & 27-224 \\\Leftrightarrow & \color{red}{2376} x& = & -197 \\\Leftrightarrow & x = \frac{-197}{2376} & & \\ & V = \left\{ \frac{-197}{2376} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{11})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -12x+\frac{20}{11}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x+ \frac{160}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{+160} & = & \color{red}{440x} +55 \\\Leftrightarrow & -1056x \color{red}{+160} \color{blue}{-160} \color{blue}{-440x} & = & \color{red}{440x} +55 \color{blue}{-440x} \color{blue}{-160} \\\Leftrightarrow & -1056x-440x& = & 55-160 \\\Leftrightarrow & \color{red}{-1496} x& = & -105 \\\Leftrightarrow & x = \frac{-105}{-1496} & & \\\Leftrightarrow & x = \frac{105}{1496} & & \\ & V = \left\{ \frac{105}{1496} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{8})& = & 9x+\frac{7}{6} \\\Leftrightarrow & 10x+\frac{25}{8}& = & 9x+\frac{7}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{240}{ \color{blue}{24} }x+ \frac{75}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{28}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 240x \color{red}{+75} & = & \color{red}{216x} +28 \\\Leftrightarrow & 240x \color{red}{+75} \color{blue}{-75} \color{blue}{-216x} & = & \color{red}{216x} +28 \color{blue}{-216x} \color{blue}{-75} \\\Leftrightarrow & 240x-216x& = & 28-75 \\\Leftrightarrow & \color{red}{24} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{24} & & \\ & V = \left\{ \frac{-47}{24} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -2x+\frac{5}{3} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -2x+\frac{5}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-48}{ \color{blue}{24} }x+ \frac{40}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+63} & = & \color{red}{-48x} +40 \\\Leftrightarrow & 504x \color{red}{+63} \color{blue}{-63} \color{blue}{+48x} & = & \color{red}{-48x} +40 \color{blue}{+48x} \color{blue}{-63} \\\Leftrightarrow & 504x+48x& = & 40-63 \\\Leftrightarrow & \color{red}{552} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{552} & & \\\Leftrightarrow & x = \frac{-1}{24} & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{9})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{28}{9}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{-308} & = & \color{red}{-891x} +54 \\\Leftrightarrow & -3465x \color{red}{-308} \color{blue}{+308} \color{blue}{+891x} & = & \color{red}{-891x} +54 \color{blue}{+891x} \color{blue}{+308} \\\Leftrightarrow & -3465x+891x& = & 54+308 \\\Leftrightarrow & \color{red}{-2574} x& = & 362 \\\Leftrightarrow & x = \frac{362}{-2574} & & \\\Leftrightarrow & x = \frac{-181}{1287} & & \\ & V = \left\{ \frac{-181}{1287} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{3})& = & 2x+\frac{3}{2} \\\Leftrightarrow & -28x-\frac{35}{3}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{70}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-70} & = & \color{red}{12x} +9 \\\Leftrightarrow & -168x \color{red}{-70} \color{blue}{+70} \color{blue}{-12x} & = & \color{red}{12x} +9 \color{blue}{-12x} \color{blue}{+70} \\\Leftrightarrow & -168x-12x& = & 9+70 \\\Leftrightarrow & \color{red}{-180} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-180} & & \\\Leftrightarrow & x = \frac{-79}{180} & & \\ & V = \left\{ \frac{-79}{180} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 16x-\frac{8}{9}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{-8} & = & \color{red}{-27x} +6 \\\Leftrightarrow & 144x \color{red}{-8} \color{blue}{+8} \color{blue}{+27x} & = & \color{red}{-27x} +6 \color{blue}{+27x} \color{blue}{+8} \\\Leftrightarrow & 144x+27x& = & 6+8 \\\Leftrightarrow & \color{red}{171} x& = & 14 \\\Leftrightarrow & x = \frac{14}{171} & & \\ & V = \left\{ \frac{14}{171} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -16x+\frac{12}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{+108} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -1584x \color{red}{+108} \color{blue}{-108} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-108} \\\Leftrightarrow & -1584x+693x& = & 110-108 \\\Leftrightarrow & \color{red}{-891} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-891} & & \\\Leftrightarrow & x = \frac{-2}{891} & & \\ & V = \left\{ \frac{-2}{891} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{6}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-18} & = & \color{red}{147x} +56 \\\Leftrightarrow & -210x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & -210x-147x& = & 56+18 \\\Leftrightarrow & \color{red}{-357} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-357} & & \\\Leftrightarrow & x = \frac{-74}{357} & & \\ & V = \left\{ \frac{-74}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+330} & = & \color{red}{385x} +63 \\\Leftrightarrow & 1386x \color{red}{+330} \color{blue}{-330} \color{blue}{-385x} & = & \color{red}{385x} +63 \color{blue}{-385x} \color{blue}{-330} \\\Leftrightarrow & 1386x-385x& = & 63-330 \\\Leftrightarrow & \color{red}{1001} x& = & -267 \\\Leftrightarrow & x = \frac{-267}{1001} & & \\ & V = \left\{ \frac{-267}{1001} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{11})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 9x-\frac{15}{11}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{-15} & = & \color{red}{55x} +10 \\\Leftrightarrow & 99x \color{red}{-15} \color{blue}{+15} \color{blue}{-55x} & = & \color{red}{55x} +10 \color{blue}{-55x} \color{blue}{+15} \\\Leftrightarrow & 99x-55x& = & 10+15 \\\Leftrightarrow & \color{red}{44} x& = & 25 \\\Leftrightarrow & x = \frac{25}{44} & & \\ & V = \left\{ \frac{25}{44} \right\} & \\\end{align}\)