Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{72x} +16 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{-72x} & = & \color{red}{72x} +16 \color{blue}{-72x} \color{blue}{-63} \\\Leftrightarrow & 336x-72x& = & 16-63 \\\Leftrightarrow & \color{red}{264} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{264} & & \\ & V = \left\{ \frac{-47}{264} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{4}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-44} & = & \color{red}{385x} +50 \\\Leftrightarrow & -550x \color{red}{-44} \color{blue}{+44} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{+44} \\\Leftrightarrow & -550x-385x& = & 50+44 \\\Leftrightarrow & \color{red}{-935} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-935} & & \\\Leftrightarrow & x = \frac{-94}{935} & & \\ & V = \left\{ \frac{-94}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & -5x+\frac{4}{9} \\\Leftrightarrow & -12x+\frac{24}{11}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{216}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+216} & = & \color{red}{-495x} +44 \\\Leftrightarrow & -1188x \color{red}{+216} \color{blue}{-216} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{-216} \\\Leftrightarrow & -1188x+495x& = & 44-216 \\\Leftrightarrow & \color{red}{-693} x& = & -172 \\\Leftrightarrow & x = \frac{-172}{-693} & & \\\Leftrightarrow & x = \frac{172}{693} & & \\ & V = \left\{ \frac{172}{693} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{7})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -15x+\frac{12}{7}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+36} & = & \color{red}{84x} +56 \\\Leftrightarrow & -315x \color{red}{+36} \color{blue}{-36} \color{blue}{-84x} & = & \color{red}{84x} +56 \color{blue}{-84x} \color{blue}{-36} \\\Leftrightarrow & -315x-84x& = & 56-36 \\\Leftrightarrow & \color{red}{-399} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-399} & & \\\Leftrightarrow & x = \frac{-20}{399} & & \\ & V = \left\{ \frac{-20}{399} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{-15} & = & \color{red}{32x} +18 \\\Leftrightarrow & -60x \color{red}{-15} \color{blue}{+15} \color{blue}{-32x} & = & \color{red}{32x} +18 \color{blue}{-32x} \color{blue}{+15} \\\Leftrightarrow & -60x-32x& = & 18+15 \\\Leftrightarrow & \color{red}{-92} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-92} & & \\\Leftrightarrow & x = \frac{-33}{92} & & \\ & V = \left\{ \frac{-33}{92} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{48}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-48} & = & \color{red}{110x} +99 \\\Leftrightarrow & -264x \color{red}{-48} \color{blue}{+48} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{+48} \\\Leftrightarrow & -264x-110x& = & 99+48 \\\Leftrightarrow & \color{red}{-374} x& = & 147 \\\Leftrightarrow & x = \frac{147}{-374} & & \\\Leftrightarrow & x = \frac{-147}{374} & & \\ & V = \left\{ \frac{-147}{374} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{7})& = & 4x+\frac{3}{7} \\\Leftrightarrow & -15x-\frac{20}{7}& = & 4x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{-20} & = & \color{red}{28x} +3 \\\Leftrightarrow & -105x \color{red}{-20} \color{blue}{+20} \color{blue}{-28x} & = & \color{red}{28x} +3 \color{blue}{-28x} \color{blue}{+20} \\\Leftrightarrow & -105x-28x& = & 3+20 \\\Leftrightarrow & \color{red}{-133} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-133} & & \\\Leftrightarrow & x = \frac{-23}{133} & & \\ & V = \left\{ \frac{-23}{133} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-220} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -1232x \color{red}{-220} \color{blue}{+220} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{+220} \\\Leftrightarrow & -1232x+539x& = & 28+220 \\\Leftrightarrow & \color{red}{-693} x& = & 248 \\\Leftrightarrow & x = \frac{248}{-693} & & \\\Leftrightarrow & x = \frac{-248}{693} & & \\ & V = \left\{ \frac{-248}{693} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -4x+\frac{10}{11}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-264}{ \color{blue}{66} }x+ \frac{60}{ \color{blue}{66} })& = & (\frac{-594}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -264x \color{red}{+60} & = & \color{red}{-594x} +55 \\\Leftrightarrow & -264x \color{red}{+60} \color{blue}{-60} \color{blue}{+594x} & = & \color{red}{-594x} +55 \color{blue}{+594x} \color{blue}{-60} \\\Leftrightarrow & -264x+594x& = & 55-60 \\\Leftrightarrow & \color{red}{330} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{330} & & \\\Leftrightarrow & x = \frac{-1}{66} & & \\ & V = \left\{ \frac{-1}{66} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{8}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{24}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-24} & = & \color{red}{147x} +28 \\\Leftrightarrow & -126x \color{red}{-24} \color{blue}{+24} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+24} \\\Leftrightarrow & -126x-147x& = & 28+24 \\\Leftrightarrow & \color{red}{-273} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-273} & & \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-54} & = & \color{red}{231x} +110 \\\Leftrightarrow & -792x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & -792x-231x& = & 110+54 \\\Leftrightarrow & \color{red}{-1023} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-1023} & & \\\Leftrightarrow & x = \frac{-164}{1023} & & \\ & V = \left\{ \frac{-164}{1023} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-4} & = & \color{red}{35x} +9 \\\Leftrightarrow & -30x \color{red}{-4} \color{blue}{+4} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{+4} \\\Leftrightarrow & -30x-35x& = & 9+4 \\\Leftrightarrow & \color{red}{-65} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-65} & & \\\Leftrightarrow & x = \frac{-1}{5} & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)