Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{8})& = & -9x+\frac{3}{5} \\\Leftrightarrow & 14x-\frac{35}{8}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x- \frac{175}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{24}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{-175} & = & \color{red}{-360x} +24 \\\Leftrightarrow & 560x \color{red}{-175} \color{blue}{+175} \color{blue}{+360x} & = & \color{red}{-360x} +24 \color{blue}{+360x} \color{blue}{+175} \\\Leftrightarrow & 560x+360x& = & 24+175 \\\Leftrightarrow & \color{red}{920} x& = & 199 \\\Leftrightarrow & x = \frac{199}{920} & & \\ & V = \left\{ \frac{199}{920} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{4})& = & -2x+\frac{9}{8} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -2x+\frac{9}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{-30} & = & \color{red}{-16x} +9 \\\Leftrightarrow & 72x \color{red}{-30} \color{blue}{+30} \color{blue}{+16x} & = & \color{red}{-16x} +9 \color{blue}{+16x} \color{blue}{+30} \\\Leftrightarrow & 72x+16x& = & 9+30 \\\Leftrightarrow & \color{red}{88} x& = & 39 \\\Leftrightarrow & x = \frac{39}{88} & & \\ & V = \left\{ \frac{39}{88} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{8})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -35x+\frac{35}{8}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{175}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+175} & = & \color{red}{120x} +36 \\\Leftrightarrow & -1400x \color{red}{+175} \color{blue}{-175} \color{blue}{-120x} & = & \color{red}{120x} +36 \color{blue}{-120x} \color{blue}{-175} \\\Leftrightarrow & -1400x-120x& = & 36-175 \\\Leftrightarrow & \color{red}{-1520} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-1520} & & \\\Leftrightarrow & x = \frac{139}{1520} & & \\ & V = \left\{ \frac{139}{1520} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{4})& = & -4x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{15}{4}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{+75} & = & \color{red}{-80x} +24 \\\Leftrightarrow & 300x \color{red}{+75} \color{blue}{-75} \color{blue}{+80x} & = & \color{red}{-80x} +24 \color{blue}{+80x} \color{blue}{-75} \\\Leftrightarrow & 300x+80x& = & 24-75 \\\Leftrightarrow & \color{red}{380} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{380} & & \\ & V = \left\{ \frac{-51}{380} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -16x-\frac{8}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x- \frac{72}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{-72} & = & \color{red}{441x} +56 \\\Leftrightarrow & -1008x \color{red}{-72} \color{blue}{+72} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{+72} \\\Leftrightarrow & -1008x-441x& = & 56+72 \\\Leftrightarrow & \color{red}{-1449} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-1449} & & \\\Leftrightarrow & x = \frac{-128}{1449} & & \\ & V = \left\{ \frac{-128}{1449} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -21x-\frac{21}{8}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -168x \color{red}{-21} & = & \color{red}{-64x} +20 \\\Leftrightarrow & -168x \color{red}{-21} \color{blue}{+21} \color{blue}{+64x} & = & \color{red}{-64x} +20 \color{blue}{+64x} \color{blue}{+21} \\\Leftrightarrow & -168x+64x& = & 20+21 \\\Leftrightarrow & \color{red}{-104} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-104} & & \\\Leftrightarrow & x = \frac{-41}{104} & & \\ & V = \left\{ \frac{-41}{104} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{7})& = & 9x+\frac{9}{11} \\\Leftrightarrow & -18x+\frac{18}{7}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{198}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+198} & = & \color{red}{693x} +63 \\\Leftrightarrow & -1386x \color{red}{+198} \color{blue}{-198} \color{blue}{-693x} & = & \color{red}{693x} +63 \color{blue}{-693x} \color{blue}{-198} \\\Leftrightarrow & -1386x-693x& = & 63-198 \\\Leftrightarrow & \color{red}{-2079} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{-2079} & & \\\Leftrightarrow & x = \frac{5}{77} & & \\ & V = \left\{ \frac{5}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{8})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 20x+\frac{15}{8}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{480}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{56}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 480x \color{red}{+45} & = & \color{red}{-168x} +56 \\\Leftrightarrow & 480x \color{red}{+45} \color{blue}{-45} \color{blue}{+168x} & = & \color{red}{-168x} +56 \color{blue}{+168x} \color{blue}{-45} \\\Leftrightarrow & 480x+168x& = & 56-45 \\\Leftrightarrow & \color{red}{648} x& = & 11 \\\Leftrightarrow & x = \frac{11}{648} & & \\ & V = \left\{ \frac{11}{648} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & -9x+\frac{10}{11} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+132} & = & \color{red}{-495x} +50 \\\Leftrightarrow & -990x \color{red}{+132} \color{blue}{-132} \color{blue}{+495x} & = & \color{red}{-495x} +50 \color{blue}{+495x} \color{blue}{-132} \\\Leftrightarrow & -990x+495x& = & 50-132 \\\Leftrightarrow & \color{red}{-495} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-495} & & \\\Leftrightarrow & x = \frac{82}{495} & & \\ & V = \left\{ \frac{82}{495} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+2)& = & -9x+\frac{2}{3} \\\Leftrightarrow & 14x-14& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x- \frac{42}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{-42} & = & \color{red}{-27x} +2 \\\Leftrightarrow & 42x \color{red}{-42} \color{blue}{+42} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{+42} \\\Leftrightarrow & 42x+27x& = & 2+42 \\\Leftrightarrow & \color{red}{69} x& = & 44 \\\Leftrightarrow & x = \frac{44}{69} & & \\ & V = \left\{ \frac{44}{69} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{8}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+24} & = & \color{red}{-105x} +70 \\\Leftrightarrow & 126x \color{red}{+24} \color{blue}{-24} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-24} \\\Leftrightarrow & 126x+105x& = & 70-24 \\\Leftrightarrow & \color{red}{231} x& = & 46 \\\Leftrightarrow & x = \frac{46}{231} & & \\ & V = \left\{ \frac{46}{231} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{3})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+100} & = & \color{red}{-45x} +18 \\\Leftrightarrow & 300x \color{red}{+100} \color{blue}{-100} \color{blue}{+45x} & = & \color{red}{-45x} +18 \color{blue}{+45x} \color{blue}{-100} \\\Leftrightarrow & 300x+45x& = & 18-100 \\\Leftrightarrow & \color{red}{345} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{345} & & \\ & V = \left\{ \frac{-82}{345} \right\} & \\\end{align}\)