Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -6x-\frac{10}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{-100} & = & \color{red}{490x} +21 \\\Leftrightarrow & -420x \color{red}{-100} \color{blue}{+100} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{+100} \\\Leftrightarrow & -420x-490x& = & 21+100 \\\Leftrightarrow & \color{red}{-910} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-910} & & \\\Leftrightarrow & x = \frac{-121}{910} & & \\ & V = \left\{ \frac{-121}{910} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{4})& = & 2x+\frac{4}{11} \\\Leftrightarrow & 15x+\frac{9}{4}& = & 2x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{660}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} })& = & (\frac{88}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 660x \color{red}{+99} & = & \color{red}{88x} +16 \\\Leftrightarrow & 660x \color{red}{+99} \color{blue}{-99} \color{blue}{-88x} & = & \color{red}{88x} +16 \color{blue}{-88x} \color{blue}{-99} \\\Leftrightarrow & 660x-88x& = & 16-99 \\\Leftrightarrow & \color{red}{572} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{572} & & \\ & V = \left\{ \frac{-83}{572} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{9}{8} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-336}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -336x \color{red}{+48} & = & \color{red}{-392x} +63 \\\Leftrightarrow & -336x \color{red}{+48} \color{blue}{-48} \color{blue}{+392x} & = & \color{red}{-392x} +63 \color{blue}{+392x} \color{blue}{-48} \\\Leftrightarrow & -336x+392x& = & 63-48 \\\Leftrightarrow & \color{red}{56} x& = & 15 \\\Leftrightarrow & x = \frac{15}{56} & & \\ & V = \left\{ \frac{15}{56} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{15}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{30}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-30} \\\Leftrightarrow & 168x+70x& = & 35-30 \\\Leftrightarrow & \color{red}{238} x& = & 5 \\\Leftrightarrow & x = \frac{5}{238} & & \\ & V = \left\{ \frac{5}{238} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{7})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -20x-\frac{12}{7}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{96}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-96} & = & \color{red}{-392x} +49 \\\Leftrightarrow & -1120x \color{red}{-96} \color{blue}{+96} \color{blue}{+392x} & = & \color{red}{-392x} +49 \color{blue}{+392x} \color{blue}{+96} \\\Leftrightarrow & -1120x+392x& = & 49+96 \\\Leftrightarrow & \color{red}{-728} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-728} & & \\\Leftrightarrow & x = \frac{-145}{728} & & \\ & V = \left\{ \frac{-145}{728} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{7})& = & -9x+\frac{5}{3} \\\Leftrightarrow & 8x+\frac{16}{7}& = & -9x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+48} & = & \color{red}{-189x} +35 \\\Leftrightarrow & 168x \color{red}{+48} \color{blue}{-48} \color{blue}{+189x} & = & \color{red}{-189x} +35 \color{blue}{+189x} \color{blue}{-48} \\\Leftrightarrow & 168x+189x& = & 35-48 \\\Leftrightarrow & \color{red}{357} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{357} & & \\ & V = \left\{ \frac{-13}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{8})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -25x+\frac{15}{8}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{+45} & = & \color{red}{-216x} +16 \\\Leftrightarrow & -600x \color{red}{+45} \color{blue}{-45} \color{blue}{+216x} & = & \color{red}{-216x} +16 \color{blue}{+216x} \color{blue}{-45} \\\Leftrightarrow & -600x+216x& = & 16-45 \\\Leftrightarrow & \color{red}{-384} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-384} & & \\\Leftrightarrow & x = \frac{29}{384} & & \\ & V = \left\{ \frac{29}{384} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{7})& = & 9x+\frac{9}{5} \\\Leftrightarrow & 4x+\frac{8}{7}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{+40} & = & \color{red}{315x} +63 \\\Leftrightarrow & 140x \color{red}{+40} \color{blue}{-40} \color{blue}{-315x} & = & \color{red}{315x} +63 \color{blue}{-315x} \color{blue}{-40} \\\Leftrightarrow & 140x-315x& = & 63-40 \\\Leftrightarrow & \color{red}{-175} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-175} & & \\\Leftrightarrow & x = \frac{-23}{175} & & \\ & V = \left\{ \frac{-23}{175} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & -4x+\frac{4}{11} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -4x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+264} & = & \color{red}{-220x} +20 \\\Leftrightarrow & -990x \color{red}{+264} \color{blue}{-264} \color{blue}{+220x} & = & \color{red}{-220x} +20 \color{blue}{+220x} \color{blue}{-264} \\\Leftrightarrow & -990x+220x& = & 20-264 \\\Leftrightarrow & \color{red}{-770} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{-770} & & \\\Leftrightarrow & x = \frac{122}{385} & & \\ & V = \left\{ \frac{122}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{9}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+99} & = & \color{red}{385x} +20 \\\Leftrightarrow & 660x \color{red}{+99} \color{blue}{-99} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{-99} \\\Leftrightarrow & 660x-385x& = & 20-99 \\\Leftrightarrow & \color{red}{275} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{275} & & \\ & V = \left\{ \frac{-79}{275} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & -8x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{6}{5}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+12} & = & \color{red}{-80x} +15 \\\Leftrightarrow & 150x \color{red}{+12} \color{blue}{-12} \color{blue}{+80x} & = & \color{red}{-80x} +15 \color{blue}{+80x} \color{blue}{-12} \\\Leftrightarrow & 150x+80x& = & 15-12 \\\Leftrightarrow & \color{red}{230} x& = & 3 \\\Leftrightarrow & x = \frac{3}{230} & & \\ & V = \left\{ \frac{3}{230} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+84} & = & \color{red}{-245x} +45 \\\Leftrightarrow & -1050x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +45 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & -1050x+245x& = & 45-84 \\\Leftrightarrow & \color{red}{-805} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-805} & & \\\Leftrightarrow & x = \frac{39}{805} & & \\ & V = \left\{ \frac{39}{805} \right\} & \\\end{align}\)