Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-396}{ \color{blue}{66} }x- \frac{36}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -396x \color{red}{-36} & = & \color{red}{-462x} +55 \\\Leftrightarrow & -396x \color{red}{-36} \color{blue}{+36} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{+36} \\\Leftrightarrow & -396x+462x& = & 55+36 \\\Leftrightarrow & \color{red}{66} x& = & 91 \\\Leftrightarrow & x = \frac{91}{66} & & \\ & V = \left\{ \frac{91}{66} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{8}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+24} & = & \color{red}{147x} +28 \\\Leftrightarrow & 420x \color{red}{+24} \color{blue}{-24} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{-24} \\\Leftrightarrow & 420x-147x& = & 28-24 \\\Leftrightarrow & \color{red}{273} x& = & 4 \\\Leftrightarrow & x = \frac{4}{273} & & \\ & V = \left\{ \frac{4}{273} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{20}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 20x \color{red}{-4} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+4} \\\Leftrightarrow & 20x+25x& = & 6+4 \\\Leftrightarrow & \color{red}{45} x& = & 10 \\\Leftrightarrow & x = \frac{10}{45} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+36} & = & \color{red}{45x} +10 \\\Leftrightarrow & 240x \color{red}{+36} \color{blue}{-36} \color{blue}{-45x} & = & \color{red}{45x} +10 \color{blue}{-45x} \color{blue}{-36} \\\Leftrightarrow & 240x-45x& = & 10-36 \\\Leftrightarrow & \color{red}{195} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{195} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{3})& = & 4x+\frac{5}{7} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 4x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-735}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -735x \color{red}{-98} & = & \color{red}{84x} +15 \\\Leftrightarrow & -735x \color{red}{-98} \color{blue}{+98} \color{blue}{-84x} & = & \color{red}{84x} +15 \color{blue}{-84x} \color{blue}{+98} \\\Leftrightarrow & -735x-84x& = & 15+98 \\\Leftrightarrow & \color{red}{-819} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-819} & & \\\Leftrightarrow & x = \frac{-113}{819} & & \\ & V = \left\{ \frac{-113}{819} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{11})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-42} & = & \color{red}{-539x} +99 \\\Leftrightarrow & -462x \color{red}{-42} \color{blue}{+42} \color{blue}{+539x} & = & \color{red}{-539x} +99 \color{blue}{+539x} \color{blue}{+42} \\\Leftrightarrow & -462x+539x& = & 99+42 \\\Leftrightarrow & \color{red}{77} x& = & 141 \\\Leftrightarrow & x = \frac{141}{77} & & \\ & V = \left\{ \frac{141}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 4x+\frac{6}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+18} & = & \color{red}{75x} +50 \\\Leftrightarrow & 60x \color{red}{+18} \color{blue}{-18} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{-18} \\\Leftrightarrow & 60x-75x& = & 50-18 \\\Leftrightarrow & \color{red}{-15} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-15} & & \\\Leftrightarrow & x = \frac{-32}{15} & & \\ & V = \left\{ \frac{-32}{15} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{8})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{25}{8}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1080}{ \color{blue}{72} }x+ \frac{225}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1080x \color{red}{+225} & = & \color{red}{504x} +64 \\\Leftrightarrow & 1080x \color{red}{+225} \color{blue}{-225} \color{blue}{-504x} & = & \color{red}{504x} +64 \color{blue}{-504x} \color{blue}{-225} \\\Leftrightarrow & 1080x-504x& = & 64-225 \\\Leftrightarrow & \color{red}{576} x& = & -161 \\\Leftrightarrow & x = \frac{-161}{576} & & \\ & V = \left\{ \frac{-161}{576} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & -350x+245x& = & 28+50 \\\Leftrightarrow & \color{red}{-105} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-105} & & \\\Leftrightarrow & x = \frac{-26}{35} & & \\ & V = \left\{ \frac{-26}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{9})& = & 8x+\frac{4}{9} \\\Leftrightarrow & 21x+\frac{28}{9}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+28} & = & \color{red}{72x} +4 \\\Leftrightarrow & 189x \color{red}{+28} \color{blue}{-28} \color{blue}{-72x} & = & \color{red}{72x} +4 \color{blue}{-72x} \color{blue}{-28} \\\Leftrightarrow & 189x-72x& = & 4-28 \\\Leftrightarrow & \color{red}{117} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{117} & & \\\Leftrightarrow & x = \frac{-8}{39} & & \\ & V = \left\{ \frac{-8}{39} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{7}{11} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{56}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-231} & = & \color{red}{-264x} +56 \\\Leftrightarrow & -1232x \color{red}{-231} \color{blue}{+231} \color{blue}{+264x} & = & \color{red}{-264x} +56 \color{blue}{+264x} \color{blue}{+231} \\\Leftrightarrow & -1232x+264x& = & 56+231 \\\Leftrightarrow & \color{red}{-968} x& = & 287 \\\Leftrightarrow & x = \frac{287}{-968} & & \\\Leftrightarrow & x = \frac{-287}{968} & & \\ & V = \left\{ \frac{-287}{968} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{7})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{4}{7}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+8} & = & \color{red}{-42x} +21 \\\Leftrightarrow & 140x \color{red}{+8} \color{blue}{-8} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{-8} \\\Leftrightarrow & 140x+42x& = & 21-8 \\\Leftrightarrow & \color{red}{182} x& = & 13 \\\Leftrightarrow & x = \frac{13}{182} & & \\\Leftrightarrow & x = \frac{1}{14} & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)