Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 15x-\frac{20}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-60} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 315x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & 315x+147x& = & 14+60 \\\Leftrightarrow & \color{red}{462} x& = & 74 \\\Leftrightarrow & x = \frac{74}{462} & & \\\Leftrightarrow & x = \frac{37}{231} & & \\ & V = \left\{ \frac{37}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{7})& = & -8x+\frac{4}{5} \\\Leftrightarrow & -15x-\frac{20}{7}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-100} & = & \color{red}{-280x} +28 \\\Leftrightarrow & -525x \color{red}{-100} \color{blue}{+100} \color{blue}{+280x} & = & \color{red}{-280x} +28 \color{blue}{+280x} \color{blue}{+100} \\\Leftrightarrow & -525x+280x& = & 28+100 \\\Leftrightarrow & \color{red}{-245} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-245} & & \\\Leftrightarrow & x = \frac{-128}{245} & & \\ & V = \left\{ \frac{-128}{245} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 21x-\frac{28}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{84}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-84} & = & \color{red}{165x} +110 \\\Leftrightarrow & 693x \color{red}{-84} \color{blue}{+84} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+84} \\\Leftrightarrow & 693x-165x& = & 110+84 \\\Leftrightarrow & \color{red}{528} x& = & 194 \\\Leftrightarrow & x = \frac{194}{528} & & \\\Leftrightarrow & x = \frac{97}{264} & & \\ & V = \left\{ \frac{97}{264} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{7})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{18}{7}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{36}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-36} & = & \color{red}{70x} +63 \\\Leftrightarrow & -168x \color{red}{-36} \color{blue}{+36} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{+36} \\\Leftrightarrow & -168x-70x& = & 63+36 \\\Leftrightarrow & \color{red}{-238} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-238} & & \\\Leftrightarrow & x = \frac{-99}{238} & & \\ & V = \left\{ \frac{-99}{238} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{15}{4}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{-105} & = & \color{red}{-140x} +36 \\\Leftrightarrow & 336x \color{red}{-105} \color{blue}{+105} \color{blue}{+140x} & = & \color{red}{-140x} +36 \color{blue}{+140x} \color{blue}{+105} \\\Leftrightarrow & 336x+140x& = & 36+105 \\\Leftrightarrow & \color{red}{476} x& = & 141 \\\Leftrightarrow & x = \frac{141}{476} & & \\ & V = \left\{ \frac{141}{476} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 9x-\frac{6}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-66} & = & \color{red}{-385x} +10 \\\Leftrightarrow & 495x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & 495x+385x& = & 10+66 \\\Leftrightarrow & \color{red}{880} x& = & 76 \\\Leftrightarrow & x = \frac{76}{880} & & \\\Leftrightarrow & x = \frac{19}{220} & & \\ & V = \left\{ \frac{19}{220} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 16x-\frac{8}{3}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{-16} & = & \color{red}{18x} +21 \\\Leftrightarrow & 96x \color{red}{-16} \color{blue}{+16} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{+16} \\\Leftrightarrow & 96x-18x& = & 21+16 \\\Leftrightarrow & \color{red}{78} x& = & 37 \\\Leftrightarrow & x = \frac{37}{78} & & \\ & V = \left\{ \frac{37}{78} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{3})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -20x+\frac{8}{3}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+16} & = & \color{red}{42x} +7 \\\Leftrightarrow & -120x \color{red}{+16} \color{blue}{-16} \color{blue}{-42x} & = & \color{red}{42x} +7 \color{blue}{-42x} \color{blue}{-16} \\\Leftrightarrow & -120x-42x& = & 7-16 \\\Leftrightarrow & \color{red}{-162} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-162} & & \\\Leftrightarrow & x = \frac{1}{18} & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{3})& = & 2x+\frac{4}{7} \\\Leftrightarrow & 21x+\frac{28}{3}& = & 2x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{+196} & = & \color{red}{42x} +12 \\\Leftrightarrow & 441x \color{red}{+196} \color{blue}{-196} \color{blue}{-42x} & = & \color{red}{42x} +12 \color{blue}{-42x} \color{blue}{-196} \\\Leftrightarrow & 441x-42x& = & 12-196 \\\Leftrightarrow & \color{red}{399} x& = & -184 \\\Leftrightarrow & x = \frac{-184}{399} & & \\ & V = \left\{ \frac{-184}{399} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 2x+\frac{6}{5} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 2x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{10}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{-9} & = & \color{red}{10x} +6 \\\Leftrightarrow & 45x \color{red}{-9} \color{blue}{+9} \color{blue}{-10x} & = & \color{red}{10x} +6 \color{blue}{-10x} \color{blue}{+9} \\\Leftrightarrow & 45x-10x& = & 6+9 \\\Leftrightarrow & \color{red}{35} x& = & 15 \\\Leftrightarrow & x = \frac{15}{35} & & \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{420}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{350x} +63 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{-60} \\\Leftrightarrow & 420x-350x& = & 63-60 \\\Leftrightarrow & \color{red}{70} x& = & 3 \\\Leftrightarrow & x = \frac{3}{70} & & \\ & V = \left\{ \frac{3}{70} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{-693x} +42 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{-110} \\\Leftrightarrow & 770x+693x& = & 42-110 \\\Leftrightarrow & \color{red}{1463} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{1463} & & \\ & V = \left\{ \frac{-68}{1463} \right\} & \\\end{align}\)