Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{2})& = & 8x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{15}{2}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{80}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{-75} & = & \color{red}{80x} +16 \\\Leftrightarrow & -150x \color{red}{-75} \color{blue}{+75} \color{blue}{-80x} & = & \color{red}{80x} +16 \color{blue}{-80x} \color{blue}{+75} \\\Leftrightarrow & -150x-80x& = & 16+75 \\\Leftrightarrow & \color{red}{-230} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-230} & & \\\Leftrightarrow & x = \frac{-91}{230} & & \\ & V = \left\{ \frac{-91}{230} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & -5x+\frac{7}{12} \\\Leftrightarrow & -4x-\frac{6}{11}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-528}{ \color{blue}{132} }x- \frac{72}{ \color{blue}{132} })& = & (\frac{-660}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -528x \color{red}{-72} & = & \color{red}{-660x} +77 \\\Leftrightarrow & -528x \color{red}{-72} \color{blue}{+72} \color{blue}{+660x} & = & \color{red}{-660x} +77 \color{blue}{+660x} \color{blue}{+72} \\\Leftrightarrow & -528x+660x& = & 77+72 \\\Leftrightarrow & \color{red}{132} x& = & 149 \\\Leftrightarrow & x = \frac{149}{132} & & \\ & V = \left\{ \frac{149}{132} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{11})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -8x+\frac{12}{11}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x+ \frac{48}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{+48} & = & \color{red}{396x} +33 \\\Leftrightarrow & -352x \color{red}{+48} \color{blue}{-48} \color{blue}{-396x} & = & \color{red}{396x} +33 \color{blue}{-396x} \color{blue}{-48} \\\Leftrightarrow & -352x-396x& = & 33-48 \\\Leftrightarrow & \color{red}{-748} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-748} & & \\\Leftrightarrow & x = \frac{15}{748} & & \\ & V = \left\{ \frac{15}{748} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{3})& = & 4x+\frac{2}{7} \\\Leftrightarrow & 25x-\frac{20}{3}& = & 4x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{-140} & = & \color{red}{84x} +6 \\\Leftrightarrow & 525x \color{red}{-140} \color{blue}{+140} \color{blue}{-84x} & = & \color{red}{84x} +6 \color{blue}{-84x} \color{blue}{+140} \\\Leftrightarrow & 525x-84x& = & 6+140 \\\Leftrightarrow & \color{red}{441} x& = & 146 \\\Leftrightarrow & x = \frac{146}{441} & & \\ & V = \left\{ \frac{146}{441} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+18} & = & \color{red}{-63x} +56 \\\Leftrightarrow & -168x \color{red}{+18} \color{blue}{-18} \color{blue}{+63x} & = & \color{red}{-63x} +56 \color{blue}{+63x} \color{blue}{-18} \\\Leftrightarrow & -168x+63x& = & 56-18 \\\Leftrightarrow & \color{red}{-105} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-105} & & \\\Leftrightarrow & x = \frac{-38}{105} & & \\ & V = \left\{ \frac{-38}{105} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -28x+\frac{21}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1260}{ \color{blue}{45} }x+ \frac{189}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1260x \color{red}{+189} & = & \color{red}{-225x} +50 \\\Leftrightarrow & -1260x \color{red}{+189} \color{blue}{-189} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{-189} \\\Leftrightarrow & -1260x+225x& = & 50-189 \\\Leftrightarrow & \color{red}{-1035} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-1035} & & \\\Leftrightarrow & x = \frac{139}{1035} & & \\ & V = \left\{ \frac{139}{1035} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{5})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 14x-\frac{21}{5}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{70}{ \color{blue}{5} }x- \frac{21}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 70x \color{red}{-21} & = & \color{red}{-25x} +7 \\\Leftrightarrow & 70x \color{red}{-21} \color{blue}{+21} \color{blue}{+25x} & = & \color{red}{-25x} +7 \color{blue}{+25x} \color{blue}{+21} \\\Leftrightarrow & 70x+25x& = & 7+21 \\\Leftrightarrow & \color{red}{95} x& = & 28 \\\Leftrightarrow & x = \frac{28}{95} & & \\ & V = \left\{ \frac{28}{95} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{5})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 4x+\frac{4}{5}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{45x} +20 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +20 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & 60x-45x& = & 20-12 \\\Leftrightarrow & \color{red}{15} x& = & 8 \\\Leftrightarrow & x = \frac{8}{15} & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{-36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & 300x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & 300x+105x& = & 20+36 \\\Leftrightarrow & \color{red}{405} x& = & 56 \\\Leftrightarrow & x = \frac{56}{405} & & \\ & V = \left\{ \frac{56}{405} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{11})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{+8} & = & \color{red}{-33x} +5 \\\Leftrightarrow & -88x \color{red}{+8} \color{blue}{-8} \color{blue}{+33x} & = & \color{red}{-33x} +5 \color{blue}{+33x} \color{blue}{-8} \\\Leftrightarrow & -88x+33x& = & 5-8 \\\Leftrightarrow & \color{red}{-55} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-55} & & \\\Leftrightarrow & x = \frac{3}{55} & & \\ & V = \left\{ \frac{3}{55} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+20} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -140x \color{red}{+20} \color{blue}{-20} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{-20} \\\Leftrightarrow & -140x+98x& = & 35-20 \\\Leftrightarrow & \color{red}{-42} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-42} & & \\\Leftrightarrow & x = \frac{-5}{14} & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{3})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -12x-\frac{8}{3}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-72}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{-30x} +7 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{+30x} & = & \color{red}{-30x} +7 \color{blue}{+30x} \color{blue}{+16} \\\Leftrightarrow & -72x+30x& = & 7+16 \\\Leftrightarrow & \color{red}{-42} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-42} & & \\\Leftrightarrow & x = \frac{-23}{42} & & \\ & V = \left\{ \frac{-23}{42} \right\} & \\\end{align}\)