Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{10})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -9x+\frac{9}{10}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{+18} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -180x \color{red}{+18} \color{blue}{-18} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{-18} \\\Leftrightarrow & -180x+100x& = & 45-18 \\\Leftrightarrow & \color{red}{-80} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-80} & & \\\Leftrightarrow & x = \frac{-27}{80} & & \\ & V = \left\{ \frac{-27}{80} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 6x+\frac{6}{5}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+6} & = & \color{red}{25x} +9 \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{-25x} & = & \color{red}{25x} +9 \color{blue}{-25x} \color{blue}{-6} \\\Leftrightarrow & 30x-25x& = & 9-6 \\\Leftrightarrow & \color{red}{5} x& = & 3 \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{16}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-48} & = & \color{red}{165x} +44 \\\Leftrightarrow & -396x \color{red}{-48} \color{blue}{+48} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{+48} \\\Leftrightarrow & -396x-165x& = & 44+48 \\\Leftrightarrow & \color{red}{-561} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-561} & & \\\Leftrightarrow & x = \frac{-92}{561} & & \\ & V = \left\{ \frac{-92}{561} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{-25x} +8 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +8 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -120x+25x& = & 8-12 \\\Leftrightarrow & \color{red}{-95} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-95} & & \\\Leftrightarrow & x = \frac{4}{95} & & \\ & V = \left\{ \frac{4}{95} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{3})& = & 2x+\frac{2}{5} \\\Leftrightarrow & 25x+\frac{25}{3}& = & 2x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{375}{ \color{blue}{15} }x+ \frac{125}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 375x \color{red}{+125} & = & \color{red}{30x} +6 \\\Leftrightarrow & 375x \color{red}{+125} \color{blue}{-125} \color{blue}{-30x} & = & \color{red}{30x} +6 \color{blue}{-30x} \color{blue}{-125} \\\Leftrightarrow & 375x-30x& = & 6-125 \\\Leftrightarrow & \color{red}{345} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{345} & & \\ & V = \left\{ \frac{-119}{345} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{7})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{-10} & = & \color{red}{21x} +6 \\\Leftrightarrow & 140x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +6 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & 140x-21x& = & 6+10 \\\Leftrightarrow & \color{red}{119} x& = & 16 \\\Leftrightarrow & x = \frac{16}{119} & & \\ & V = \left\{ \frac{16}{119} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-150} & = & \color{red}{-175x} +21 \\\Leftrightarrow & 630x \color{red}{-150} \color{blue}{+150} \color{blue}{+175x} & = & \color{red}{-175x} +21 \color{blue}{+175x} \color{blue}{+150} \\\Leftrightarrow & 630x+175x& = & 21+150 \\\Leftrightarrow & \color{red}{805} x& = & 171 \\\Leftrightarrow & x = \frac{171}{805} & & \\ & V = \left\{ \frac{171}{805} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{3})& = & 9x+\frac{9}{10} \\\Leftrightarrow & -4x-\frac{10}{3}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-120}{ \color{blue}{30} }x- \frac{100}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -120x \color{red}{-100} & = & \color{red}{270x} +27 \\\Leftrightarrow & -120x \color{red}{-100} \color{blue}{+100} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+100} \\\Leftrightarrow & -120x-270x& = & 27+100 \\\Leftrightarrow & \color{red}{-390} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-390} & & \\\Leftrightarrow & x = \frac{-127}{390} & & \\ & V = \left\{ \frac{-127}{390} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{2})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -20x+\frac{15}{2}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+105} & = & \color{red}{-42x} +8 \\\Leftrightarrow & -280x \color{red}{+105} \color{blue}{-105} \color{blue}{+42x} & = & \color{red}{-42x} +8 \color{blue}{+42x} \color{blue}{-105} \\\Leftrightarrow & -280x+42x& = & 8-105 \\\Leftrightarrow & \color{red}{-238} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-238} & & \\\Leftrightarrow & x = \frac{97}{238} & & \\ & V = \left\{ \frac{97}{238} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{3})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -16x-\frac{16}{3}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x- \frac{32}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{-32} & = & \color{red}{42x} +5 \\\Leftrightarrow & -96x \color{red}{-32} \color{blue}{+32} \color{blue}{-42x} & = & \color{red}{42x} +5 \color{blue}{-42x} \color{blue}{+32} \\\Leftrightarrow & -96x-42x& = & 5+32 \\\Leftrightarrow & \color{red}{-138} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-138} & & \\\Leftrightarrow & x = \frac{-37}{138} & & \\ & V = \left\{ \frac{-37}{138} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -12x+\frac{6}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+42} & = & \color{red}{-175x} +30 \\\Leftrightarrow & -420x \color{red}{+42} \color{blue}{-42} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{-42} \\\Leftrightarrow & -420x+175x& = & 30-42 \\\Leftrightarrow & \color{red}{-245} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-245} & & \\\Leftrightarrow & x = \frac{12}{245} & & \\ & V = \left\{ \frac{12}{245} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{25}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{100}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-100} & = & \color{red}{196x} +21 \\\Leftrightarrow & -280x \color{red}{-100} \color{blue}{+100} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{+100} \\\Leftrightarrow & -280x-196x& = & 21+100 \\\Leftrightarrow & \color{red}{-476} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-476} & & \\\Leftrightarrow & x = \frac{-121}{476} & & \\ & V = \left\{ \frac{-121}{476} \right\} & \\\end{align}\)