Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{2})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{15}{2}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x- \frac{60}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{-60} & = & \color{red}{-40x} +7 \\\Leftrightarrow & -96x \color{red}{-60} \color{blue}{+60} \color{blue}{+40x} & = & \color{red}{-40x} +7 \color{blue}{+40x} \color{blue}{+60} \\\Leftrightarrow & -96x+40x& = & 7+60 \\\Leftrightarrow & \color{red}{-56} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-56} & & \\\Leftrightarrow & x = \frac{-67}{56} & & \\ & V = \left\{ \frac{-67}{56} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{4})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{+75} & = & \color{red}{-140x} +24 \\\Leftrightarrow & -120x \color{red}{+75} \color{blue}{-75} \color{blue}{+140x} & = & \color{red}{-140x} +24 \color{blue}{+140x} \color{blue}{-75} \\\Leftrightarrow & -120x+140x& = & 24-75 \\\Leftrightarrow & \color{red}{20} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{20} & & \\ & V = \left\{ \frac{-51}{20} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{11})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -12x+\frac{16}{11}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{64}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+64} & = & \color{red}{220x} +55 \\\Leftrightarrow & -528x \color{red}{+64} \color{blue}{-64} \color{blue}{-220x} & = & \color{red}{220x} +55 \color{blue}{-220x} \color{blue}{-64} \\\Leftrightarrow & -528x-220x& = & 55-64 \\\Leftrightarrow & \color{red}{-748} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-748} & & \\\Leftrightarrow & x = \frac{9}{748} & & \\ & V = \left\{ \frac{9}{748} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+132} & = & \color{red}{385x} +10 \\\Leftrightarrow & -330x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & -330x-385x& = & 10-132 \\\Leftrightarrow & \color{red}{-715} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-715} & & \\\Leftrightarrow & x = \frac{122}{715} & & \\ & V = \left\{ \frac{122}{715} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{11})& = & -4x+\frac{10}{11} \\\Leftrightarrow & 15x-\frac{6}{11}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-6} & = & \color{red}{-44x} +10 \\\Leftrightarrow & 165x \color{red}{-6} \color{blue}{+6} \color{blue}{+44x} & = & \color{red}{-44x} +10 \color{blue}{+44x} \color{blue}{+6} \\\Leftrightarrow & 165x+44x& = & 10+6 \\\Leftrightarrow & \color{red}{209} x& = & 16 \\\Leftrightarrow & x = \frac{16}{209} & & \\ & V = \left\{ \frac{16}{209} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{10}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+50} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -150x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & -150x+105x& = & 18-50 \\\Leftrightarrow & \color{red}{-45} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-45} & & \\\Leftrightarrow & x = \frac{32}{45} & & \\ & V = \left\{ \frac{32}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+10} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -70x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -70x+49x& = & 9-10 \\\Leftrightarrow & \color{red}{-21} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-21} & & \\\Leftrightarrow & x = \frac{1}{21} & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+10} & = & \color{red}{49x} +10 \\\Leftrightarrow & 70x \color{red}{+10} \color{blue}{-10} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-10} \\\Leftrightarrow & 70x-49x& = & 10-10 \\\Leftrightarrow & \color{red}{21} x& = & 0 \\\Leftrightarrow & x = \frac{0}{21} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 4x+\frac{6}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 44x \color{red}{+6} & = & \color{red}{55x} +8 \\\Leftrightarrow & 44x \color{red}{+6} \color{blue}{-6} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{-6} \\\Leftrightarrow & 44x-55x& = & 8-6 \\\Leftrightarrow & \color{red}{-11} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-11} & & \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-160}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -160x \color{red}{+24} & = & \color{red}{70x} +7 \\\Leftrightarrow & -160x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +7 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -160x-70x& = & 7-24 \\\Leftrightarrow & \color{red}{-230} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-230} & & \\\Leftrightarrow & x = \frac{17}{230} & & \\ & V = \left\{ \frac{17}{230} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{6}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+30} \\\Leftrightarrow & 330x+275x& = & 66+30 \\\Leftrightarrow & \color{red}{605} x& = & 96 \\\Leftrightarrow & x = \frac{96}{605} & & \\ & V = \left\{ \frac{96}{605} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{7})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{15}{7}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{30}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{-56x} +21 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{+56x} & = & \color{red}{-56x} +21 \color{blue}{+56x} \color{blue}{+30} \\\Leftrightarrow & -210x+56x& = & 21+30 \\\Leftrightarrow & \color{red}{-154} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-154} & & \\\Leftrightarrow & x = \frac{-51}{154} & & \\ & V = \left\{ \frac{-51}{154} \right\} & \\\end{align}\)