Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{+108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -720x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -720x+315x& = & 50-108 \\\Leftrightarrow & \color{red}{-405} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-405} & & \\\Leftrightarrow & x = \frac{58}{405} & & \\ & V = \left\{ \frac{58}{405} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{25x} +6 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & -60x-25x& = & 6+12 \\\Leftrightarrow & \color{red}{-85} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-85} & & \\\Leftrightarrow & x = \frac{-18}{85} & & \\ & V = \left\{ \frac{-18}{85} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{6})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 10x-\frac{25}{6}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{420}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{126x} +36 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{-126x} & = & \color{red}{126x} +36 \color{blue}{-126x} \color{blue}{+175} \\\Leftrightarrow & 420x-126x& = & 36+175 \\\Leftrightarrow & \color{red}{294} x& = & 211 \\\Leftrightarrow & x = \frac{211}{294} & & \\ & V = \left\{ \frac{211}{294} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{5})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 8x-\frac{8}{5}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x- \frac{32}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{-32} & = & \color{red}{-140x} +45 \\\Leftrightarrow & 160x \color{red}{-32} \color{blue}{+32} \color{blue}{+140x} & = & \color{red}{-140x} +45 \color{blue}{+140x} \color{blue}{+32} \\\Leftrightarrow & 160x+140x& = & 45+32 \\\Leftrightarrow & \color{red}{300} x& = & 77 \\\Leftrightarrow & x = \frac{77}{300} & & \\ & V = \left\{ \frac{77}{300} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{11})& = & 6x+\frac{7}{8} \\\Leftrightarrow & -35x+\frac{21}{11}& = & 6x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-3080}{ \color{blue}{88} }x+ \frac{168}{ \color{blue}{88} })& = & (\frac{528}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -3080x \color{red}{+168} & = & \color{red}{528x} +77 \\\Leftrightarrow & -3080x \color{red}{+168} \color{blue}{-168} \color{blue}{-528x} & = & \color{red}{528x} +77 \color{blue}{-528x} \color{blue}{-168} \\\Leftrightarrow & -3080x-528x& = & 77-168 \\\Leftrightarrow & \color{red}{-3608} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{-3608} & & \\\Leftrightarrow & x = \frac{91}{3608} & & \\ & V = \left\{ \frac{91}{3608} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 6x-\frac{12}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-36} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 198x \color{red}{-36} \color{blue}{+36} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{+36} \\\Leftrightarrow & 198x+165x& = & 44+36 \\\Leftrightarrow & \color{red}{363} x& = & 80 \\\Leftrightarrow & x = \frac{80}{363} & & \\ & V = \left\{ \frac{80}{363} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{8}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+88} & = & \color{red}{-231x} +18 \\\Leftrightarrow & -330x \color{red}{+88} \color{blue}{-88} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{-88} \\\Leftrightarrow & -330x+231x& = & 18-88 \\\Leftrightarrow & \color{red}{-99} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{-99} & & \\\Leftrightarrow & x = \frac{70}{99} & & \\ & V = \left\{ \frac{70}{99} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-54} & = & \color{red}{-567x} +14 \\\Leftrightarrow & 504x \color{red}{-54} \color{blue}{+54} \color{blue}{+567x} & = & \color{red}{-567x} +14 \color{blue}{+567x} \color{blue}{+54} \\\Leftrightarrow & 504x+567x& = & 14+54 \\\Leftrightarrow & \color{red}{1071} x& = & 68 \\\Leftrightarrow & x = \frac{68}{1071} & & \\\Leftrightarrow & x = \frac{4}{63} & & \\ & V = \left\{ \frac{4}{63} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{40x} +12 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{-40x} & = & \color{red}{40x} +12 \color{blue}{-40x} \color{blue}{-21} \\\Leftrightarrow & 112x-40x& = & 12-21 \\\Leftrightarrow & \color{red}{72} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{72} & & \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+36} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 90x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 90x+75x& = & 20-36 \\\Leftrightarrow & \color{red}{165} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{165} & & \\ & V = \left\{ \frac{-16}{165} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 9x+\frac{4}{7} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{784}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 784x \color{red}{+147} & = & \color{red}{504x} +32 \\\Leftrightarrow & 784x \color{red}{+147} \color{blue}{-147} \color{blue}{-504x} & = & \color{red}{504x} +32 \color{blue}{-504x} \color{blue}{-147} \\\Leftrightarrow & 784x-504x& = & 32-147 \\\Leftrightarrow & \color{red}{280} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{280} & & \\\Leftrightarrow & x = \frac{-23}{56} & & \\ & V = \left\{ \frac{-23}{56} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{3})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -6x-\frac{8}{3}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-88} & = & \color{red}{231x} +30 \\\Leftrightarrow & -198x \color{red}{-88} \color{blue}{+88} \color{blue}{-231x} & = & \color{red}{231x} +30 \color{blue}{-231x} \color{blue}{+88} \\\Leftrightarrow & -198x-231x& = & 30+88 \\\Leftrightarrow & \color{red}{-429} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-429} & & \\\Leftrightarrow & x = \frac{-118}{429} & & \\ & V = \left\{ \frac{-118}{429} \right\} & \\\end{align}\)