Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -4x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -4x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-18} & = & \color{red}{-84x} +70 \\\Leftrightarrow & 315x \color{red}{-18} \color{blue}{+18} \color{blue}{+84x} & = & \color{red}{-84x} +70 \color{blue}{+84x} \color{blue}{+18} \\\Leftrightarrow & 315x+84x& = & 70+18 \\\Leftrightarrow & \color{red}{399} x& = & 88 \\\Leftrightarrow & x = \frac{88}{399} & & \\ & V = \left\{ \frac{88}{399} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{7})& = & -8x+\frac{7}{3} \\\Leftrightarrow & 9x+\frac{9}{7}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{+27} & = & \color{red}{-168x} +49 \\\Leftrightarrow & 189x \color{red}{+27} \color{blue}{-27} \color{blue}{+168x} & = & \color{red}{-168x} +49 \color{blue}{+168x} \color{blue}{-27} \\\Leftrightarrow & 189x+168x& = & 49-27 \\\Leftrightarrow & \color{red}{357} x& = & 22 \\\Leftrightarrow & x = \frac{22}{357} & & \\ & V = \left\{ \frac{22}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & 2x+\frac{2}{3} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{+54} & = & \color{red}{66x} +22 \\\Leftrightarrow & -594x \color{red}{+54} \color{blue}{-54} \color{blue}{-66x} & = & \color{red}{66x} +22 \color{blue}{-66x} \color{blue}{-54} \\\Leftrightarrow & -594x-66x& = & 22-54 \\\Leftrightarrow & \color{red}{-660} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-660} & & \\\Leftrightarrow & x = \frac{8}{165} & & \\ & V = \left\{ \frac{8}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{30}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+30} & = & \color{red}{-55x} +6 \\\Leftrightarrow & -132x \color{red}{+30} \color{blue}{-30} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-30} \\\Leftrightarrow & -132x+55x& = & 6-30 \\\Leftrightarrow & \color{red}{-77} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-77} & & \\\Leftrightarrow & x = \frac{24}{77} & & \\ & V = \left\{ \frac{24}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{6})& = & 4x+\frac{9}{4} \\\Leftrightarrow & -15x-\frac{25}{6}& = & 4x+\frac{9}{4} \\ & & & \text{kgv van noemers 6 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{50}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-50} & = & \color{red}{48x} +27 \\\Leftrightarrow & -180x \color{red}{-50} \color{blue}{+50} \color{blue}{-48x} & = & \color{red}{48x} +27 \color{blue}{-48x} \color{blue}{+50} \\\Leftrightarrow & -180x-48x& = & 27+50 \\\Leftrightarrow & \color{red}{-228} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-228} & & \\\Leftrightarrow & x = \frac{-77}{228} & & \\ & V = \left\{ \frac{-77}{228} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{5})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 14x-\frac{14}{5}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{490}{ \color{blue}{35} }x- \frac{98}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 490x \color{red}{-98} & = & \color{red}{-315x} +40 \\\Leftrightarrow & 490x \color{red}{-98} \color{blue}{+98} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{+98} \\\Leftrightarrow & 490x+315x& = & 40+98 \\\Leftrightarrow & \color{red}{805} x& = & 138 \\\Leftrightarrow & x = \frac{138}{805} & & \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -12x+\frac{18}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x+ \frac{108}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{+108} & = & \color{red}{-150x} +25 \\\Leftrightarrow & -360x \color{red}{+108} \color{blue}{-108} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{-108} \\\Leftrightarrow & -360x+150x& = & 25-108 \\\Leftrightarrow & \color{red}{-210} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-210} & & \\\Leftrightarrow & x = \frac{83}{210} & & \\ & V = \left\{ \frac{83}{210} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 150x \color{red}{+12} \color{blue}{-12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-12} \\\Leftrightarrow & 150x-35x& = & 6-12 \\\Leftrightarrow & \color{red}{115} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{115} & & \\ & V = \left\{ \frac{-6}{115} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{147x} +14 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & -126x-147x& = & 14-30 \\\Leftrightarrow & \color{red}{-273} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-273} & & \\\Leftrightarrow & x = \frac{16}{273} & & \\ & V = \left\{ \frac{16}{273} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{11})& = & 2x+\frac{3}{5} \\\Leftrightarrow & 15x+\frac{6}{11}& = & 2x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+30} & = & \color{red}{110x} +33 \\\Leftrightarrow & 825x \color{red}{+30} \color{blue}{-30} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{-30} \\\Leftrightarrow & 825x-110x& = & 33-30 \\\Leftrightarrow & \color{red}{715} x& = & 3 \\\Leftrightarrow & x = \frac{3}{715} & & \\ & V = \left\{ \frac{3}{715} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -16x-\frac{8}{9}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{-8} & = & \color{red}{63x} +10 \\\Leftrightarrow & -144x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & -144x-63x& = & 10+8 \\\Leftrightarrow & \color{red}{-207} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-207} & & \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{3})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{20}{3}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{-20} & = & \color{red}{15x} +8 \\\Leftrightarrow & -36x \color{red}{-20} \color{blue}{+20} \color{blue}{-15x} & = & \color{red}{15x} +8 \color{blue}{-15x} \color{blue}{+20} \\\Leftrightarrow & -36x-15x& = & 8+20 \\\Leftrightarrow & \color{red}{-51} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-51} & & \\\Leftrightarrow & x = \frac{-28}{51} & & \\ & V = \left\{ \frac{-28}{51} \right\} & \\\end{align}\)