Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+1)& = & 3x+\frac{2}{11} \\\Leftrightarrow & -28x-7& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x- \frac{77}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{-77} & = & \color{red}{33x} +2 \\\Leftrightarrow & -308x \color{red}{-77} \color{blue}{+77} \color{blue}{-33x} & = & \color{red}{33x} +2 \color{blue}{-33x} \color{blue}{+77} \\\Leftrightarrow & -308x-33x& = & 2+77 \\\Leftrightarrow & \color{red}{-341} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-341} & & \\\Leftrightarrow & x = \frac{-79}{341} & & \\ & V = \left\{ \frac{-79}{341} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{11})& = & 3x+\frac{3}{4} \\\Leftrightarrow & -8x+\frac{4}{11}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{+16} & = & \color{red}{132x} +33 \\\Leftrightarrow & -352x \color{red}{+16} \color{blue}{-16} \color{blue}{-132x} & = & \color{red}{132x} +33 \color{blue}{-132x} \color{blue}{-16} \\\Leftrightarrow & -352x-132x& = & 33-16 \\\Leftrightarrow & \color{red}{-484} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-484} & & \\\Leftrightarrow & x = \frac{-17}{484} & & \\ & V = \left\{ \frac{-17}{484} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & 5x+\frac{7}{4} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{100x} +35 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +35 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & -240x-100x& = & 35+48 \\\Leftrightarrow & \color{red}{-340} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-340} & & \\\Leftrightarrow & x = \frac{-83}{340} & & \\ & V = \left\{ \frac{-83}{340} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+54} & = & \color{red}{165x} +44 \\\Leftrightarrow & -396x \color{red}{+54} \color{blue}{-54} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-54} \\\Leftrightarrow & -396x-165x& = & 44-54 \\\Leftrightarrow & \color{red}{-561} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-561} & & \\\Leftrightarrow & x = \frac{10}{561} & & \\ & V = \left\{ \frac{10}{561} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{15}{8}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{+45} & = & \color{red}{72x} +64 \\\Leftrightarrow & -480x \color{red}{+45} \color{blue}{-45} \color{blue}{-72x} & = & \color{red}{72x} +64 \color{blue}{-72x} \color{blue}{-45} \\\Leftrightarrow & -480x-72x& = & 64-45 \\\Leftrightarrow & \color{red}{-552} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-552} & & \\\Leftrightarrow & x = \frac{-19}{552} & & \\ & V = \left\{ \frac{-19}{552} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{3})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-40} & = & \color{red}{-45x} +24 \\\Leftrightarrow & -300x \color{red}{-40} \color{blue}{+40} \color{blue}{+45x} & = & \color{red}{-45x} +24 \color{blue}{+45x} \color{blue}{+40} \\\Leftrightarrow & -300x+45x& = & 24+40 \\\Leftrightarrow & \color{red}{-255} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-255} & & \\\Leftrightarrow & x = \frac{-64}{255} & & \\ & V = \left\{ \frac{-64}{255} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & -330x+231x& = & 110+30 \\\Leftrightarrow & \color{red}{-99} x& = & 140 \\\Leftrightarrow & x = \frac{140}{-99} & & \\\Leftrightarrow & x = \frac{-140}{99} & & \\ & V = \left\{ \frac{-140}{99} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{7})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -8x-\frac{8}{7}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x- \frac{48}{ \color{blue}{42} })& = & (\frac{378}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{378x} +35 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{-378x} & = & \color{red}{378x} +35 \color{blue}{-378x} \color{blue}{+48} \\\Leftrightarrow & -336x-378x& = & 35+48 \\\Leftrightarrow & \color{red}{-714} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-714} & & \\\Leftrightarrow & x = \frac{-83}{714} & & \\ & V = \left\{ \frac{-83}{714} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{9})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -10x+\frac{4}{9}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{+20} & = & \color{red}{-315x} +72 \\\Leftrightarrow & -450x \color{red}{+20} \color{blue}{-20} \color{blue}{+315x} & = & \color{red}{-315x} +72 \color{blue}{+315x} \color{blue}{-20} \\\Leftrightarrow & -450x+315x& = & 72-20 \\\Leftrightarrow & \color{red}{-135} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-135} & & \\\Leftrightarrow & x = \frac{-52}{135} & & \\ & V = \left\{ \frac{-52}{135} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{7})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{+80} & = & \color{red}{392x} +49 \\\Leftrightarrow & -560x \color{red}{+80} \color{blue}{-80} \color{blue}{-392x} & = & \color{red}{392x} +49 \color{blue}{-392x} \color{blue}{-80} \\\Leftrightarrow & -560x-392x& = & 49-80 \\\Leftrightarrow & \color{red}{-952} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-952} & & \\\Leftrightarrow & x = \frac{31}{952} & & \\ & V = \left\{ \frac{31}{952} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{7})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 8x-\frac{20}{7}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x- \frac{80}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{-80} & = & \color{red}{84x} +21 \\\Leftrightarrow & 224x \color{red}{-80} \color{blue}{+80} \color{blue}{-84x} & = & \color{red}{84x} +21 \color{blue}{-84x} \color{blue}{+80} \\\Leftrightarrow & 224x-84x& = & 21+80 \\\Leftrightarrow & \color{red}{140} x& = & 101 \\\Leftrightarrow & x = \frac{101}{140} & & \\ & V = \left\{ \frac{101}{140} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & -9x+\frac{9}{4} \\\Leftrightarrow & 16x+\frac{20}{3}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{192}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 192x \color{red}{+80} & = & \color{red}{-108x} +27 \\\Leftrightarrow & 192x \color{red}{+80} \color{blue}{-80} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{-80} \\\Leftrightarrow & 192x+108x& = & 27-80 \\\Leftrightarrow & \color{red}{300} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{300} & & \\ & V = \left\{ \frac{-53}{300} \right\} & \\\end{align}\)