Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & -8x+\frac{10}{11} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{-165} & = & \color{red}{-352x} +40 \\\Leftrightarrow & -660x \color{red}{-165} \color{blue}{+165} \color{blue}{+352x} & = & \color{red}{-352x} +40 \color{blue}{+352x} \color{blue}{+165} \\\Leftrightarrow & -660x+352x& = & 40+165 \\\Leftrightarrow & \color{red}{-308} x& = & 205 \\\Leftrightarrow & x = \frac{205}{-308} & & \\\Leftrightarrow & x = \frac{-205}{308} & & \\ & V = \left\{ \frac{-205}{308} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{3})& = & 4x+\frac{5}{12} \\\Leftrightarrow & 35x-\frac{35}{3}& = & 4x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x- \frac{140}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{-140} & = & \color{red}{48x} +5 \\\Leftrightarrow & 420x \color{red}{-140} \color{blue}{+140} \color{blue}{-48x} & = & \color{red}{48x} +5 \color{blue}{-48x} \color{blue}{+140} \\\Leftrightarrow & 420x-48x& = & 5+140 \\\Leftrightarrow & \color{red}{372} x& = & 145 \\\Leftrightarrow & x = \frac{145}{372} & & \\ & V = \left\{ \frac{145}{372} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{+32} & = & \color{red}{70x} +63 \\\Leftrightarrow & -168x \color{red}{+32} \color{blue}{-32} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{-32} \\\Leftrightarrow & -168x-70x& = & 63-32 \\\Leftrightarrow & \color{red}{-238} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-238} & & \\\Leftrightarrow & x = \frac{-31}{238} & & \\ & V = \left\{ \frac{-31}{238} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-960}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -960x \color{red}{-192} & = & \color{red}{200x} +45 \\\Leftrightarrow & -960x \color{red}{-192} \color{blue}{+192} \color{blue}{-200x} & = & \color{red}{200x} +45 \color{blue}{-200x} \color{blue}{+192} \\\Leftrightarrow & -960x-200x& = & 45+192 \\\Leftrightarrow & \color{red}{-1160} x& = & 237 \\\Leftrightarrow & x = \frac{237}{-1160} & & \\\Leftrightarrow & x = \frac{-237}{1160} & & \\ & V = \left\{ \frac{-237}{1160} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{11})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -9x-\frac{6}{11}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-30} & = & \color{red}{-275x} +22 \\\Leftrightarrow & -495x \color{red}{-30} \color{blue}{+30} \color{blue}{+275x} & = & \color{red}{-275x} +22 \color{blue}{+275x} \color{blue}{+30} \\\Leftrightarrow & -495x+275x& = & 22+30 \\\Leftrightarrow & \color{red}{-220} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-220} & & \\\Leftrightarrow & x = \frac{-13}{55} & & \\ & V = \left\{ \frac{-13}{55} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{7})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-10} & = & \color{red}{21x} +2 \\\Leftrightarrow & 56x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & 56x-21x& = & 2+10 \\\Leftrightarrow & \color{red}{35} x& = & 12 \\\Leftrightarrow & x = \frac{12}{35} & & \\ & V = \left\{ \frac{12}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & -420x+147x& = & 28+60 \\\Leftrightarrow & \color{red}{-273} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-273} & & \\\Leftrightarrow & x = \frac{-88}{273} & & \\ & V = \left\{ \frac{-88}{273} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{7})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 24x-\frac{24}{7}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{672}{ \color{blue}{28} }x- \frac{96}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 672x \color{red}{-96} & = & \color{red}{-140x} +21 \\\Leftrightarrow & 672x \color{red}{-96} \color{blue}{+96} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{+96} \\\Leftrightarrow & 672x+140x& = & 21+96 \\\Leftrightarrow & \color{red}{812} x& = & 117 \\\Leftrightarrow & x = \frac{117}{812} & & \\ & V = \left\{ \frac{117}{812} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{4}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{20}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-20} & = & \color{red}{315x} +42 \\\Leftrightarrow & 140x \color{red}{-20} \color{blue}{+20} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+20} \\\Leftrightarrow & 140x-315x& = & 42+20 \\\Leftrightarrow & \color{red}{-175} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-175} & & \\\Leftrightarrow & x = \frac{-62}{175} & & \\ & V = \left\{ \frac{-62}{175} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & -2x+\frac{6}{7} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-56}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{+105} & = & \color{red}{-56x} +24 \\\Leftrightarrow & 700x \color{red}{+105} \color{blue}{-105} \color{blue}{+56x} & = & \color{red}{-56x} +24 \color{blue}{+56x} \color{blue}{-105} \\\Leftrightarrow & 700x+56x& = & 24-105 \\\Leftrightarrow & \color{red}{756} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{756} & & \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{5})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+36} & = & \color{red}{120x} +20 \\\Leftrightarrow & -225x \color{red}{+36} \color{blue}{-36} \color{blue}{-120x} & = & \color{red}{120x} +20 \color{blue}{-120x} \color{blue}{-36} \\\Leftrightarrow & -225x-120x& = & 20-36 \\\Leftrightarrow & \color{red}{-345} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-345} & & \\\Leftrightarrow & x = \frac{16}{345} & & \\ & V = \left\{ \frac{16}{345} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{7})& = & 3x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{4}{7}& = & 3x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x- \frac{16}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{-16} & = & \color{red}{84x} +49 \\\Leftrightarrow & 280x \color{red}{-16} \color{blue}{+16} \color{blue}{-84x} & = & \color{red}{84x} +49 \color{blue}{-84x} \color{blue}{+16} \\\Leftrightarrow & 280x-84x& = & 49+16 \\\Leftrightarrow & \color{red}{196} x& = & 65 \\\Leftrightarrow & x = \frac{65}{196} & & \\ & V = \left\{ \frac{65}{196} \right\} & \\\end{align}\)