Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 8x+\frac{6}{5}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+54} & = & \color{red}{135x} +50 \\\Leftrightarrow & 360x \color{red}{+54} \color{blue}{-54} \color{blue}{-135x} & = & \color{red}{135x} +50 \color{blue}{-135x} \color{blue}{-54} \\\Leftrightarrow & 360x-135x& = & 50-54 \\\Leftrightarrow & \color{red}{225} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{225} & & \\ & V = \left\{ \frac{-4}{225} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{9})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 12x-\frac{8}{9}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{864}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 864x \color{red}{-64} & = & \color{red}{-360x} +45 \\\Leftrightarrow & 864x \color{red}{-64} \color{blue}{+64} \color{blue}{+360x} & = & \color{red}{-360x} +45 \color{blue}{+360x} \color{blue}{+64} \\\Leftrightarrow & 864x+360x& = & 45+64 \\\Leftrightarrow & \color{red}{1224} x& = & 109 \\\Leftrightarrow & x = \frac{109}{1224} & & \\ & V = \left\{ \frac{109}{1224} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-32} & = & \color{red}{98x} +63 \\\Leftrightarrow & 280x \color{red}{-32} \color{blue}{+32} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{+32} \\\Leftrightarrow & 280x-98x& = & 63+32 \\\Leftrightarrow & \color{red}{182} x& = & 95 \\\Leftrightarrow & x = \frac{95}{182} & & \\ & V = \left\{ \frac{95}{182} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{6})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{-125} & = & \color{red}{210x} +36 \\\Leftrightarrow & 600x \color{red}{-125} \color{blue}{+125} \color{blue}{-210x} & = & \color{red}{210x} +36 \color{blue}{-210x} \color{blue}{+125} \\\Leftrightarrow & 600x-210x& = & 36+125 \\\Leftrightarrow & \color{red}{390} x& = & 161 \\\Leftrightarrow & x = \frac{161}{390} & & \\ & V = \left\{ \frac{161}{390} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{7})& = & -3x+\frac{2}{5} \\\Leftrightarrow & 10x+\frac{8}{7}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+40} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 350x \color{red}{+40} \color{blue}{-40} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{-40} \\\Leftrightarrow & 350x+105x& = & 14-40 \\\Leftrightarrow & \color{red}{455} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{455} & & \\\Leftrightarrow & x = \frac{-2}{35} & & \\ & V = \left\{ \frac{-2}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 4x-\frac{10}{7}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{224}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 224x \color{red}{-80} & = & \color{red}{168x} +49 \\\Leftrightarrow & 224x \color{red}{-80} \color{blue}{+80} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{+80} \\\Leftrightarrow & 224x-168x& = & 49+80 \\\Leftrightarrow & \color{red}{56} x& = & 129 \\\Leftrightarrow & x = \frac{129}{56} & & \\ & V = \left\{ \frac{129}{56} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-48}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -48x \color{red}{+8} & = & \color{red}{21x} +4 \\\Leftrightarrow & -48x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & -48x-21x& = & 4-8 \\\Leftrightarrow & \color{red}{-69} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-69} & & \\\Leftrightarrow & x = \frac{4}{69} & & \\ & V = \left\{ \frac{4}{69} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & -5x+\frac{7}{11} \\\Leftrightarrow & -25x+\frac{10}{7}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+110} & = & \color{red}{-385x} +49 \\\Leftrightarrow & -1925x \color{red}{+110} \color{blue}{-110} \color{blue}{+385x} & = & \color{red}{-385x} +49 \color{blue}{+385x} \color{blue}{-110} \\\Leftrightarrow & -1925x+385x& = & 49-110 \\\Leftrightarrow & \color{red}{-1540} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-1540} & & \\\Leftrightarrow & x = \frac{61}{1540} & & \\ & V = \left\{ \frac{61}{1540} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-84} & = & \color{red}{-175x} +40 \\\Leftrightarrow & 630x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 630x+175x& = & 40+84 \\\Leftrightarrow & \color{red}{805} x& = & 124 \\\Leftrightarrow & x = \frac{124}{805} & & \\ & V = \left\{ \frac{124}{805} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{9})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 10x-\frac{10}{9}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x- \frac{50}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{-50} & = & \color{red}{-315x} +81 \\\Leftrightarrow & 450x \color{red}{-50} \color{blue}{+50} \color{blue}{+315x} & = & \color{red}{-315x} +81 \color{blue}{+315x} \color{blue}{+50} \\\Leftrightarrow & 450x+315x& = & 81+50 \\\Leftrightarrow & \color{red}{765} x& = & 131 \\\Leftrightarrow & x = \frac{131}{765} & & \\ & V = \left\{ \frac{131}{765} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{16}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x+ \frac{32}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{+32} & = & \color{red}{110x} +99 \\\Leftrightarrow & 176x \color{red}{+32} \color{blue}{-32} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{-32} \\\Leftrightarrow & 176x-110x& = & 99-32 \\\Leftrightarrow & \color{red}{66} x& = & 67 \\\Leftrightarrow & x = \frac{67}{66} & & \\ & V = \left\{ \frac{67}{66} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{11})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -14x-\frac{21}{11}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x- \frac{42}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{-42} & = & \color{red}{110x} +55 \\\Leftrightarrow & -308x \color{red}{-42} \color{blue}{+42} \color{blue}{-110x} & = & \color{red}{110x} +55 \color{blue}{-110x} \color{blue}{+42} \\\Leftrightarrow & -308x-110x& = & 55+42 \\\Leftrightarrow & \color{red}{-418} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-418} & & \\\Leftrightarrow & x = \frac{-97}{418} & & \\ & V = \left\{ \frac{-97}{418} \right\} & \\\end{align}\)