Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 8x-\frac{16}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-144} & = & \color{red}{315x} +70 \\\Leftrightarrow & 504x \color{red}{-144} \color{blue}{+144} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{+144} \\\Leftrightarrow & 504x-315x& = & 70+144 \\\Leftrightarrow & \color{red}{189} x& = & 214 \\\Leftrightarrow & x = \frac{214}{189} & & \\ & V = \left\{ \frac{214}{189} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{5})& = & -3x+\frac{5}{11} \\\Leftrightarrow & 28x+\frac{14}{5}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{+154} & = & \color{red}{-165x} +25 \\\Leftrightarrow & 1540x \color{red}{+154} \color{blue}{-154} \color{blue}{+165x} & = & \color{red}{-165x} +25 \color{blue}{+165x} \color{blue}{-154} \\\Leftrightarrow & 1540x+165x& = & 25-154 \\\Leftrightarrow & \color{red}{1705} x& = & -129 \\\Leftrightarrow & x = \frac{-129}{1705} & & \\ & V = \left\{ \frac{-129}{1705} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{2})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -21x+\frac{21}{2}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{+63} & = & \color{red}{48x} +16 \\\Leftrightarrow & -126x \color{red}{+63} \color{blue}{-63} \color{blue}{-48x} & = & \color{red}{48x} +16 \color{blue}{-48x} \color{blue}{-63} \\\Leftrightarrow & -126x-48x& = & 16-63 \\\Leftrightarrow & \color{red}{-174} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-174} & & \\\Leftrightarrow & x = \frac{47}{174} & & \\ & V = \left\{ \frac{47}{174} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{+50} & = & \color{red}{280x} +42 \\\Leftrightarrow & 875x \color{red}{+50} \color{blue}{-50} \color{blue}{-280x} & = & \color{red}{280x} +42 \color{blue}{-280x} \color{blue}{-50} \\\Leftrightarrow & 875x-280x& = & 42-50 \\\Leftrightarrow & \color{red}{595} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{595} & & \\ & V = \left\{ \frac{-8}{595} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{+108} & = & \color{red}{225x} +20 \\\Leftrightarrow & 540x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +20 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & 540x-225x& = & 20-108 \\\Leftrightarrow & \color{red}{315} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{315} & & \\ & V = \left\{ \frac{-88}{315} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & -7x+\frac{5}{4} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{+24} & = & \color{red}{-196x} +35 \\\Leftrightarrow & 168x \color{red}{+24} \color{blue}{-24} \color{blue}{+196x} & = & \color{red}{-196x} +35 \color{blue}{+196x} \color{blue}{-24} \\\Leftrightarrow & 168x+196x& = & 35-24 \\\Leftrightarrow & \color{red}{364} x& = & 11 \\\Leftrightarrow & x = \frac{11}{364} & & \\ & V = \left\{ \frac{11}{364} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -16x-\frac{20}{3}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-100} & = & \color{red}{105x} +12 \\\Leftrightarrow & -240x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & -240x-105x& = & 12+100 \\\Leftrightarrow & \color{red}{-345} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-345} & & \\\Leftrightarrow & x = \frac{-112}{345} & & \\ & V = \left\{ \frac{-112}{345} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-18} & = & \color{red}{99x} +10 \\\Leftrightarrow & -198x \color{red}{-18} \color{blue}{+18} \color{blue}{-99x} & = & \color{red}{99x} +10 \color{blue}{-99x} \color{blue}{+18} \\\Leftrightarrow & -198x-99x& = & 10+18 \\\Leftrightarrow & \color{red}{-297} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-297} & & \\\Leftrightarrow & x = \frac{-28}{297} & & \\ & V = \left\{ \frac{-28}{297} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 90x+70x& = & 45-24 \\\Leftrightarrow & \color{red}{160} x& = & 21 \\\Leftrightarrow & x = \frac{21}{160} & & \\ & V = \left\{ \frac{21}{160} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+6} & = & \color{red}{49x} +10 \\\Leftrightarrow & -42x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & -42x-49x& = & 10-6 \\\Leftrightarrow & \color{red}{-91} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-91} & & \\\Leftrightarrow & x = \frac{-4}{91} & & \\ & V = \left\{ \frac{-4}{91} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{7})& = & -4x+\frac{9}{8} \\\Leftrightarrow & 9x-\frac{9}{7}& = & -4x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{504}{ \color{blue}{56} }x- \frac{72}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 504x \color{red}{-72} & = & \color{red}{-224x} +63 \\\Leftrightarrow & 504x \color{red}{-72} \color{blue}{+72} \color{blue}{+224x} & = & \color{red}{-224x} +63 \color{blue}{+224x} \color{blue}{+72} \\\Leftrightarrow & 504x+224x& = & 63+72 \\\Leftrightarrow & \color{red}{728} x& = & 135 \\\Leftrightarrow & x = \frac{135}{728} & & \\ & V = \left\{ \frac{135}{728} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x-\frac{12}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-132} & = & \color{red}{539x} +42 \\\Leftrightarrow & -2310x \color{red}{-132} \color{blue}{+132} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+132} \\\Leftrightarrow & -2310x-539x& = & 42+132 \\\Leftrightarrow & \color{red}{-2849} x& = & 174 \\\Leftrightarrow & x = \frac{174}{-2849} & & \\\Leftrightarrow & x = \frac{-174}{2849} & & \\ & V = \left\{ \frac{-174}{2849} \right\} & \\\end{align}\)