Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{4}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{+20} & = & \color{red}{-315x} +54 \\\Leftrightarrow & -450x \color{red}{+20} \color{blue}{-20} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{-20} \\\Leftrightarrow & -450x+315x& = & 54-20 \\\Leftrightarrow & \color{red}{-135} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-135} & & \\\Leftrightarrow & x = \frac{-34}{135} & & \\ & V = \left\{ \frac{-34}{135} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{7})& = & 4x+\frac{7}{6} \\\Leftrightarrow & 15x-\frac{15}{7}& = & 4x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x- \frac{90}{ \color{blue}{42} })& = & (\frac{168}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{168x} +49 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{+90} \\\Leftrightarrow & 630x-168x& = & 49+90 \\\Leftrightarrow & \color{red}{462} x& = & 139 \\\Leftrightarrow & x = \frac{139}{462} & & \\ & V = \left\{ \frac{139}{462} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{20}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+40} & = & \color{red}{-70x} +63 \\\Leftrightarrow & 168x \color{red}{+40} \color{blue}{-40} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{-40} \\\Leftrightarrow & 168x+70x& = & 63-40 \\\Leftrightarrow & \color{red}{238} x& = & 23 \\\Leftrightarrow & x = \frac{23}{238} & & \\ & V = \left\{ \frac{23}{238} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{4})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 6x+\frac{15}{4}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{48}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 48x \color{red}{+30} & = & \color{red}{-40x} +5 \\\Leftrightarrow & 48x \color{red}{+30} \color{blue}{-30} \color{blue}{+40x} & = & \color{red}{-40x} +5 \color{blue}{+40x} \color{blue}{-30} \\\Leftrightarrow & 48x+40x& = & 5-30 \\\Leftrightarrow & \color{red}{88} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{88} & & \\ & V = \left\{ \frac{-25}{88} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{3})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -10x+\frac{4}{3}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{42x} +5 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{-42x} & = & \color{red}{42x} +5 \color{blue}{-42x} \color{blue}{-8} \\\Leftrightarrow & -60x-42x& = & 5-8 \\\Leftrightarrow & \color{red}{-102} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-102} & & \\\Leftrightarrow & x = \frac{1}{34} & & \\ & V = \left\{ \frac{1}{34} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{15}{4}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{-165} & = & \color{red}{220x} +24 \\\Leftrightarrow & 528x \color{red}{-165} \color{blue}{+165} \color{blue}{-220x} & = & \color{red}{220x} +24 \color{blue}{-220x} \color{blue}{+165} \\\Leftrightarrow & 528x-220x& = & 24+165 \\\Leftrightarrow & \color{red}{308} x& = & 189 \\\Leftrightarrow & x = \frac{189}{308} & & \\\Leftrightarrow & x = \frac{27}{44} & & \\ & V = \left\{ \frac{27}{44} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-2)& = & 8x+\frac{10}{7} \\\Leftrightarrow & -21x+14& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-147}{ \color{blue}{7} }x+ \frac{98}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -147x \color{red}{+98} & = & \color{red}{56x} +10 \\\Leftrightarrow & -147x \color{red}{+98} \color{blue}{-98} \color{blue}{-56x} & = & \color{red}{56x} +10 \color{blue}{-56x} \color{blue}{-98} \\\Leftrightarrow & -147x-56x& = & 10-98 \\\Leftrightarrow & \color{red}{-203} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-203} & & \\\Leftrightarrow & x = \frac{88}{203} & & \\ & V = \left\{ \frac{88}{203} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{11})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 30x-\frac{24}{11}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{-216} & = & \color{red}{-693x} +44 \\\Leftrightarrow & 2970x \color{red}{-216} \color{blue}{+216} \color{blue}{+693x} & = & \color{red}{-693x} +44 \color{blue}{+693x} \color{blue}{+216} \\\Leftrightarrow & 2970x+693x& = & 44+216 \\\Leftrightarrow & \color{red}{3663} x& = & 260 \\\Leftrightarrow & x = \frac{260}{3663} & & \\ & V = \left\{ \frac{260}{3663} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{5})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -4x+\frac{6}{5}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-80}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -80x \color{red}{+24} & = & \color{red}{100x} +15 \\\Leftrightarrow & -80x \color{red}{+24} \color{blue}{-24} \color{blue}{-100x} & = & \color{red}{100x} +15 \color{blue}{-100x} \color{blue}{-24} \\\Leftrightarrow & -80x-100x& = & 15-24 \\\Leftrightarrow & \color{red}{-180} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-180} & & \\\Leftrightarrow & x = \frac{1}{20} & & \\ & V = \left\{ \frac{1}{20} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{12})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -21x+\frac{35}{12}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x+ \frac{35}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{+35} & = & \color{red}{-96x} +8 \\\Leftrightarrow & -252x \color{red}{+35} \color{blue}{-35} \color{blue}{+96x} & = & \color{red}{-96x} +8 \color{blue}{+96x} \color{blue}{-35} \\\Leftrightarrow & -252x+96x& = & 8-35 \\\Leftrightarrow & \color{red}{-156} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-156} & & \\\Leftrightarrow & x = \frac{9}{52} & & \\ & V = \left\{ \frac{9}{52} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{6}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-42} & = & \color{red}{245x} +50 \\\Leftrightarrow & 350x \color{red}{-42} \color{blue}{+42} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{+42} \\\Leftrightarrow & 350x-245x& = & 50+42 \\\Leftrightarrow & \color{red}{105} x& = & 92 \\\Leftrightarrow & x = \frac{92}{105} & & \\ & V = \left\{ \frac{92}{105} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{11})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 18x-\frac{24}{11}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{-216} & = & \color{red}{-495x} +22 \\\Leftrightarrow & 1782x \color{red}{-216} \color{blue}{+216} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{+216} \\\Leftrightarrow & 1782x+495x& = & 22+216 \\\Leftrightarrow & \color{red}{2277} x& = & 238 \\\Leftrightarrow & x = \frac{238}{2277} & & \\ & V = \left\{ \frac{238}{2277} \right\} & \\\end{align}\)