Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -21x+\frac{28}{3}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{+196} & = & \color{red}{-168x} +27 \\\Leftrightarrow & -441x \color{red}{+196} \color{blue}{-196} \color{blue}{+168x} & = & \color{red}{-168x} +27 \color{blue}{+168x} \color{blue}{-196} \\\Leftrightarrow & -441x+168x& = & 27-196 \\\Leftrightarrow & \color{red}{-273} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-273} & & \\\Leftrightarrow & x = \frac{13}{21} & & \\ & V = \left\{ \frac{13}{21} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+264} & = & \color{red}{-275x} +30 \\\Leftrightarrow & -990x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & -990x+275x& = & 30-264 \\\Leftrightarrow & \color{red}{-715} x& = & -234 \\\Leftrightarrow & x = \frac{-234}{-715} & & \\\Leftrightarrow & x = \frac{18}{55} & & \\ & V = \left\{ \frac{18}{55} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{6}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-42} & = & \color{red}{245x} +50 \\\Leftrightarrow & 350x \color{red}{-42} \color{blue}{+42} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{+42} \\\Leftrightarrow & 350x-245x& = & 50+42 \\\Leftrightarrow & \color{red}{105} x& = & 92 \\\Leftrightarrow & x = \frac{92}{105} & & \\ & V = \left\{ \frac{92}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & -630x+147x& = & 56-90 \\\Leftrightarrow & \color{red}{-483} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-483} & & \\\Leftrightarrow & x = \frac{34}{483} & & \\ & V = \left\{ \frac{34}{483} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & -5x+\frac{7}{3} \\\Leftrightarrow & 4x-\frac{6}{5}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{-75x} +35 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{+75x} & = & \color{red}{-75x} +35 \color{blue}{+75x} \color{blue}{+18} \\\Leftrightarrow & 60x+75x& = & 35+18 \\\Leftrightarrow & \color{red}{135} x& = & 53 \\\Leftrightarrow & x = \frac{53}{135} & & \\ & V = \left\{ \frac{53}{135} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{-6} & = & \color{red}{-21x} +3 \\\Leftrightarrow & 28x \color{red}{-6} \color{blue}{+6} \color{blue}{+21x} & = & \color{red}{-21x} +3 \color{blue}{+21x} \color{blue}{+6} \\\Leftrightarrow & 28x+21x& = & 3+6 \\\Leftrightarrow & \color{red}{49} x& = & 9 \\\Leftrightarrow & x = \frac{9}{49} & & \\ & V = \left\{ \frac{9}{49} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{8})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 14x-\frac{35}{8}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x- \frac{35}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{-35} & = & \color{red}{-40x} +36 \\\Leftrightarrow & 112x \color{red}{-35} \color{blue}{+35} \color{blue}{+40x} & = & \color{red}{-40x} +36 \color{blue}{+40x} \color{blue}{+35} \\\Leftrightarrow & 112x+40x& = & 36+35 \\\Leftrightarrow & \color{red}{152} x& = & 71 \\\Leftrightarrow & x = \frac{71}{152} & & \\ & V = \left\{ \frac{71}{152} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{7})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{-10} & = & \color{red}{-35x} +3 \\\Leftrightarrow & 42x \color{red}{-10} \color{blue}{+10} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{+10} \\\Leftrightarrow & 42x+35x& = & 3+10 \\\Leftrightarrow & \color{red}{77} x& = & 13 \\\Leftrightarrow & x = \frac{13}{77} & & \\ & V = \left\{ \frac{13}{77} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{7})& = & 3x+\frac{9}{5} \\\Leftrightarrow & -8x-\frac{10}{7}& = & 3x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-50} & = & \color{red}{105x} +63 \\\Leftrightarrow & -280x \color{red}{-50} \color{blue}{+50} \color{blue}{-105x} & = & \color{red}{105x} +63 \color{blue}{-105x} \color{blue}{+50} \\\Leftrightarrow & -280x-105x& = & 63+50 \\\Leftrightarrow & \color{red}{-385} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-385} & & \\\Leftrightarrow & x = \frac{-113}{385} & & \\ & V = \left\{ \frac{-113}{385} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{5})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 20x+\frac{8}{5}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+72} & = & \color{red}{405x} +20 \\\Leftrightarrow & 900x \color{red}{+72} \color{blue}{-72} \color{blue}{-405x} & = & \color{red}{405x} +20 \color{blue}{-405x} \color{blue}{-72} \\\Leftrightarrow & 900x-405x& = & 20-72 \\\Leftrightarrow & \color{red}{495} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{495} & & \\ & V = \left\{ \frac{-52}{495} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{5})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -6x+\frac{8}{5}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-240}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -240x \color{red}{+64} & = & \color{red}{280x} +15 \\\Leftrightarrow & -240x \color{red}{+64} \color{blue}{-64} \color{blue}{-280x} & = & \color{red}{280x} +15 \color{blue}{-280x} \color{blue}{-64} \\\Leftrightarrow & -240x-280x& = & 15-64 \\\Leftrightarrow & \color{red}{-520} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-520} & & \\\Leftrightarrow & x = \frac{49}{520} & & \\ & V = \left\{ \frac{49}{520} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{11})& = & -2x+\frac{4}{5} \\\Leftrightarrow & -25x+\frac{15}{11}& = & -2x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1375}{ \color{blue}{55} }x+ \frac{75}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1375x \color{red}{+75} & = & \color{red}{-110x} +44 \\\Leftrightarrow & -1375x \color{red}{+75} \color{blue}{-75} \color{blue}{+110x} & = & \color{red}{-110x} +44 \color{blue}{+110x} \color{blue}{-75} \\\Leftrightarrow & -1375x+110x& = & 44-75 \\\Leftrightarrow & \color{red}{-1265} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-1265} & & \\\Leftrightarrow & x = \frac{31}{1265} & & \\ & V = \left\{ \frac{31}{1265} \right\} & \\\end{align}\)