Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{5})& = & 6x+\frac{3}{10} \\\Leftrightarrow & -35x-\frac{14}{5}& = & 6x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-350}{ \color{blue}{10} }x- \frac{28}{ \color{blue}{10} })& = & (\frac{60}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -350x \color{red}{-28} & = & \color{red}{60x} +3 \\\Leftrightarrow & -350x \color{red}{-28} \color{blue}{+28} \color{blue}{-60x} & = & \color{red}{60x} +3 \color{blue}{-60x} \color{blue}{+28} \\\Leftrightarrow & -350x-60x& = & 3+28 \\\Leftrightarrow & \color{red}{-410} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-410} & & \\\Leftrightarrow & x = \frac{-31}{410} & & \\ & V = \left\{ \frac{-31}{410} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{11})& = & 2x+\frac{8}{11} \\\Leftrightarrow & 9x+\frac{15}{11}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{+15} & = & \color{red}{22x} +8 \\\Leftrightarrow & 99x \color{red}{+15} \color{blue}{-15} \color{blue}{-22x} & = & \color{red}{22x} +8 \color{blue}{-22x} \color{blue}{-15} \\\Leftrightarrow & 99x-22x& = & 8-15 \\\Leftrightarrow & \color{red}{77} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{77} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{-21} & = & \color{red}{24x} +12 \\\Leftrightarrow & 224x \color{red}{-21} \color{blue}{+21} \color{blue}{-24x} & = & \color{red}{24x} +12 \color{blue}{-24x} \color{blue}{+21} \\\Leftrightarrow & 224x-24x& = & 12+21 \\\Leftrightarrow & \color{red}{200} x& = & 33 \\\Leftrightarrow & x = \frac{33}{200} & & \\ & V = \left\{ \frac{33}{200} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -10x-\frac{25}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{50}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-50} & = & \color{red}{98x} +49 \\\Leftrightarrow & -140x \color{red}{-50} \color{blue}{+50} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+50} \\\Leftrightarrow & -140x-98x& = & 49+50 \\\Leftrightarrow & \color{red}{-238} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-238} & & \\\Leftrightarrow & x = \frac{-99}{238} & & \\ & V = \left\{ \frac{-99}{238} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{792}{ \color{blue}{66} }x+ \frac{108}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 792x \color{red}{+108} & = & \color{red}{-330x} +77 \\\Leftrightarrow & 792x \color{red}{+108} \color{blue}{-108} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{-108} \\\Leftrightarrow & 792x+330x& = & 77-108 \\\Leftrightarrow & \color{red}{1122} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{1122} & & \\ & V = \left\{ \frac{-31}{1122} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{7})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 25x-\frac{15}{7}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x- \frac{75}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{-75} & = & \color{red}{-70x} +42 \\\Leftrightarrow & 875x \color{red}{-75} \color{blue}{+75} \color{blue}{+70x} & = & \color{red}{-70x} +42 \color{blue}{+70x} \color{blue}{+75} \\\Leftrightarrow & 875x+70x& = & 42+75 \\\Leftrightarrow & \color{red}{945} x& = & 117 \\\Leftrightarrow & x = \frac{117}{945} & & \\\Leftrightarrow & x = \frac{13}{105} & & \\ & V = \left\{ \frac{13}{105} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{8})& = & -4x+\frac{4}{7} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-105} & = & \color{red}{-224x} +32 \\\Leftrightarrow & -840x \color{red}{-105} \color{blue}{+105} \color{blue}{+224x} & = & \color{red}{-224x} +32 \color{blue}{+224x} \color{blue}{+105} \\\Leftrightarrow & -840x+224x& = & 32+105 \\\Leftrightarrow & \color{red}{-616} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-616} & & \\\Leftrightarrow & x = \frac{-137}{616} & & \\ & V = \left\{ \frac{-137}{616} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{12}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{12}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+12} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -42x \color{red}{+12} \color{blue}{-12} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-12} \\\Leftrightarrow & -42x+49x& = & 10-12 \\\Leftrightarrow & \color{red}{7} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{7})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -20x-\frac{8}{7}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{40}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-40} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -700x \color{red}{-40} \color{blue}{+40} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+40} \\\Leftrightarrow & -700x+315x& = & 56+40 \\\Leftrightarrow & \color{red}{-385} x& = & 96 \\\Leftrightarrow & x = \frac{96}{-385} & & \\\Leftrightarrow & x = \frac{-96}{385} & & \\ & V = \left\{ \frac{-96}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{2})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 9x-\frac{15}{2}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x- \frac{60}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{-60} & = & \color{red}{-40x} +7 \\\Leftrightarrow & 72x \color{red}{-60} \color{blue}{+60} \color{blue}{+40x} & = & \color{red}{-40x} +7 \color{blue}{+40x} \color{blue}{+60} \\\Leftrightarrow & 72x+40x& = & 7+60 \\\Leftrightarrow & \color{red}{112} x& = & 67 \\\Leftrightarrow & x = \frac{67}{112} & & \\ & V = \left\{ \frac{67}{112} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 16x+\frac{20}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+60} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 336x \color{red}{+60} \color{blue}{-60} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-60} \\\Leftrightarrow & 336x+147x& = & 70-60 \\\Leftrightarrow & \color{red}{483} x& = & 10 \\\Leftrightarrow & x = \frac{10}{483} & & \\ & V = \left\{ \frac{10}{483} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -16x-\frac{16}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-176}{ \color{blue}{11} }x- \frac{16}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -176x \color{red}{-16} & = & \color{red}{77x} +4 \\\Leftrightarrow & -176x \color{red}{-16} \color{blue}{+16} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{+16} \\\Leftrightarrow & -176x-77x& = & 4+16 \\\Leftrightarrow & \color{red}{-253} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-253} & & \\\Leftrightarrow & x = \frac{-20}{253} & & \\ & V = \left\{ \frac{-20}{253} \right\} & \\\end{align}\)