Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{11})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-84} & = & \color{red}{-539x} +99 \\\Leftrightarrow & 924x \color{red}{-84} \color{blue}{+84} \color{blue}{+539x} & = & \color{red}{-539x} +99 \color{blue}{+539x} \color{blue}{+84} \\\Leftrightarrow & 924x+539x& = & 99+84 \\\Leftrightarrow & \color{red}{1463} x& = & 183 \\\Leftrightarrow & x = \frac{183}{1463} & & \\ & V = \left\{ \frac{183}{1463} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{7})& = & 3x+\frac{3}{5} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 3x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{105x} +21 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +21 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & 700x-105x& = & 21+100 \\\Leftrightarrow & \color{red}{595} x& = & 121 \\\Leftrightarrow & x = \frac{121}{595} & & \\ & V = \left\{ \frac{121}{595} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 18x-\frac{24}{5}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-24} & = & \color{red}{-35x} +2 \\\Leftrightarrow & 90x \color{red}{-24} \color{blue}{+24} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{+24} \\\Leftrightarrow & 90x+35x& = & 2+24 \\\Leftrightarrow & \color{red}{125} x& = & 26 \\\Leftrightarrow & x = \frac{26}{125} & & \\ & V = \left\{ \frac{26}{125} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 8x+\frac{16}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{48}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+48} & = & \color{red}{105x} +50 \\\Leftrightarrow & 120x \color{red}{+48} \color{blue}{-48} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-48} \\\Leftrightarrow & 120x-105x& = & 50-48 \\\Leftrightarrow & \color{red}{15} x& = & 2 \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-110} \\\Leftrightarrow & 770x+539x& = & 42-110 \\\Leftrightarrow & \color{red}{1309} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{1309} & & \\\Leftrightarrow & x = \frac{-4}{77} & & \\ & V = \left\{ \frac{-4}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & -5x+\frac{9}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-275x} +45 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +45 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 660x+275x& = & 45+132 \\\Leftrightarrow & \color{red}{935} x& = & 177 \\\Leftrightarrow & x = \frac{177}{935} & & \\ & V = \left\{ \frac{177}{935} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 20x-\frac{25}{6}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{-125} & = & \color{red}{-210x} +24 \\\Leftrightarrow & 600x \color{red}{-125} \color{blue}{+125} \color{blue}{+210x} & = & \color{red}{-210x} +24 \color{blue}{+210x} \color{blue}{+125} \\\Leftrightarrow & 600x+210x& = & 24+125 \\\Leftrightarrow & \color{red}{810} x& = & 149 \\\Leftrightarrow & x = \frac{149}{810} & & \\ & V = \left\{ \frac{149}{810} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-45} & = & \color{red}{-84x} +16 \\\Leftrightarrow & -240x \color{red}{-45} \color{blue}{+45} \color{blue}{+84x} & = & \color{red}{-84x} +16 \color{blue}{+84x} \color{blue}{+45} \\\Leftrightarrow & -240x+84x& = & 16+45 \\\Leftrightarrow & \color{red}{-156} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-156} & & \\\Leftrightarrow & x = \frac{-61}{156} & & \\ & V = \left\{ \frac{-61}{156} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{9})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{4}{9}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+28} & = & \color{red}{-441x} +27 \\\Leftrightarrow & 504x \color{red}{+28} \color{blue}{-28} \color{blue}{+441x} & = & \color{red}{-441x} +27 \color{blue}{+441x} \color{blue}{-28} \\\Leftrightarrow & 504x+441x& = & 27-28 \\\Leftrightarrow & \color{red}{945} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{945} & & \\ & V = \left\{ \frac{-1}{945} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{3})& = & 4x+\frac{3}{2} \\\Leftrightarrow & -28x+\frac{14}{3}& = & 4x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{24}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+28} & = & \color{red}{24x} +9 \\\Leftrightarrow & -168x \color{red}{+28} \color{blue}{-28} \color{blue}{-24x} & = & \color{red}{24x} +9 \color{blue}{-24x} \color{blue}{-28} \\\Leftrightarrow & -168x-24x& = & 9-28 \\\Leftrightarrow & \color{red}{-192} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-192} & & \\\Leftrightarrow & x = \frac{19}{192} & & \\ & V = \left\{ \frac{19}{192} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{11})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 8x-\frac{10}{11}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-70} & = & \color{red}{-385x} +33 \\\Leftrightarrow & 616x \color{red}{-70} \color{blue}{+70} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{+70} \\\Leftrightarrow & 616x+385x& = & 33+70 \\\Leftrightarrow & \color{red}{1001} x& = & 103 \\\Leftrightarrow & x = \frac{103}{1001} & & \\ & V = \left\{ \frac{103}{1001} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x-\frac{30}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-270} & = & \color{red}{495x} +110 \\\Leftrightarrow & -1188x \color{red}{-270} \color{blue}{+270} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{+270} \\\Leftrightarrow & -1188x-495x& = & 110+270 \\\Leftrightarrow & \color{red}{-1683} x& = & 380 \\\Leftrightarrow & x = \frac{380}{-1683} & & \\\Leftrightarrow & x = \frac{-380}{1683} & & \\ & V = \left\{ \frac{-380}{1683} \right\} & \\\end{align}\)