Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{3})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -4x+\frac{10}{3}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+50} & = & \color{red}{-75x} +6 \\\Leftrightarrow & -60x \color{red}{+50} \color{blue}{-50} \color{blue}{+75x} & = & \color{red}{-75x} +6 \color{blue}{+75x} \color{blue}{-50} \\\Leftrightarrow & -60x+75x& = & 6-50 \\\Leftrightarrow & \color{red}{15} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{15} & & \\ & V = \left\{ \frac{-44}{15} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+330} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -1386x \color{red}{+330} \color{blue}{-330} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-330} \\\Leftrightarrow & -1386x+539x& = & 42-330 \\\Leftrightarrow & \color{red}{-847} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{-847} & & \\\Leftrightarrow & x = \frac{288}{847} & & \\ & V = \left\{ \frac{288}{847} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -4x+\frac{6}{7} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-84} & = & \color{red}{-140x} +30 \\\Leftrightarrow & -525x \color{red}{-84} \color{blue}{+84} \color{blue}{+140x} & = & \color{red}{-140x} +30 \color{blue}{+140x} \color{blue}{+84} \\\Leftrightarrow & -525x+140x& = & 30+84 \\\Leftrightarrow & \color{red}{-385} x& = & 114 \\\Leftrightarrow & x = \frac{114}{-385} & & \\\Leftrightarrow & x = \frac{-114}{385} & & \\ & V = \left\{ \frac{-114}{385} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-30} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -550x \color{red}{-30} \color{blue}{+30} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+30} \\\Leftrightarrow & -550x+385x& = & 66+30 \\\Leftrightarrow & \color{red}{-165} x& = & 96 \\\Leftrightarrow & x = \frac{96}{-165} & & \\\Leftrightarrow & x = \frac{-32}{55} & & \\ & V = \left\{ \frac{-32}{55} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 18x+\frac{30}{7}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{+270} & = & \color{red}{-315x} +35 \\\Leftrightarrow & 1134x \color{red}{+270} \color{blue}{-270} \color{blue}{+315x} & = & \color{red}{-315x} +35 \color{blue}{+315x} \color{blue}{-270} \\\Leftrightarrow & 1134x+315x& = & 35-270 \\\Leftrightarrow & \color{red}{1449} x& = & -235 \\\Leftrightarrow & x = \frac{-235}{1449} & & \\ & V = \left\{ \frac{-235}{1449} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{15}{4}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{+45} & = & \color{red}{-36x} +32 \\\Leftrightarrow & 240x \color{red}{+45} \color{blue}{-45} \color{blue}{+36x} & = & \color{red}{-36x} +32 \color{blue}{+36x} \color{blue}{-45} \\\Leftrightarrow & 240x+36x& = & 32-45 \\\Leftrightarrow & \color{red}{276} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{276} & & \\ & V = \left\{ \frac{-13}{276} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{-25x} +8 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{+25x} & = & \color{red}{-25x} +8 \color{blue}{+25x} \color{blue}{+24} \\\Leftrightarrow & 60x+25x& = & 8+24 \\\Leftrightarrow & \color{red}{85} x& = & 32 \\\Leftrightarrow & x = \frac{32}{85} & & \\ & V = \left\{ \frac{32}{85} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{7})& = & 4x+\frac{10}{7} \\\Leftrightarrow & -15x-\frac{9}{7}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x- \frac{9}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{-9} & = & \color{red}{28x} +10 \\\Leftrightarrow & -105x \color{red}{-9} \color{blue}{+9} \color{blue}{-28x} & = & \color{red}{28x} +10 \color{blue}{-28x} \color{blue}{+9} \\\Leftrightarrow & -105x-28x& = & 10+9 \\\Leftrightarrow & \color{red}{-133} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-133} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{225x} +20 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +20 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & -540x-225x& = & 20-108 \\\Leftrightarrow & \color{red}{-765} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-765} & & \\\Leftrightarrow & x = \frac{88}{765} & & \\ & V = \left\{ \frac{88}{765} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 18x-\frac{30}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-210} & = & \color{red}{-385x} +44 \\\Leftrightarrow & 1386x \color{red}{-210} \color{blue}{+210} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+210} \\\Leftrightarrow & 1386x+385x& = & 44+210 \\\Leftrightarrow & \color{red}{1771} x& = & 254 \\\Leftrightarrow & x = \frac{254}{1771} & & \\ & V = \left\{ \frac{254}{1771} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{+24} & = & \color{red}{70x} +9 \\\Leftrightarrow & -90x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +9 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -90x-70x& = & 9-24 \\\Leftrightarrow & \color{red}{-160} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-160} & & \\\Leftrightarrow & x = \frac{3}{32} & & \\ & V = \left\{ \frac{3}{32} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -8x+\frac{6}{5}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+12} & = & \color{red}{90x} +45 \\\Leftrightarrow & -80x \color{red}{+12} \color{blue}{-12} \color{blue}{-90x} & = & \color{red}{90x} +45 \color{blue}{-90x} \color{blue}{-12} \\\Leftrightarrow & -80x-90x& = & 45-12 \\\Leftrightarrow & \color{red}{-170} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-170} & & \\\Leftrightarrow & x = \frac{-33}{170} & & \\ & V = \left\{ \frac{-33}{170} \right\} & \\\end{align}\)