Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{3})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 16x+\frac{20}{3}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+140} & = & \color{red}{189x} +24 \\\Leftrightarrow & 336x \color{red}{+140} \color{blue}{-140} \color{blue}{-189x} & = & \color{red}{189x} +24 \color{blue}{-189x} \color{blue}{-140} \\\Leftrightarrow & 336x-189x& = & 24-140 \\\Leftrightarrow & \color{red}{147} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{147} & & \\ & V = \left\{ \frac{-116}{147} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{4})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{15}{4}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -500x \color{red}{-75} & = & \color{red}{-100x} +24 \\\Leftrightarrow & -500x \color{red}{-75} \color{blue}{+75} \color{blue}{+100x} & = & \color{red}{-100x} +24 \color{blue}{+100x} \color{blue}{+75} \\\Leftrightarrow & -500x+100x& = & 24+75 \\\Leftrightarrow & \color{red}{-400} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-400} & & \\\Leftrightarrow & x = \frac{-99}{400} & & \\ & V = \left\{ \frac{-99}{400} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{8})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -6x+\frac{15}{8}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-144}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{14}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -144x \color{red}{+45} & = & \color{red}{168x} +14 \\\Leftrightarrow & -144x \color{red}{+45} \color{blue}{-45} \color{blue}{-168x} & = & \color{red}{168x} +14 \color{blue}{-168x} \color{blue}{-45} \\\Leftrightarrow & -144x-168x& = & 14-45 \\\Leftrightarrow & \color{red}{-312} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-312} & & \\\Leftrightarrow & x = \frac{31}{312} & & \\ & V = \left\{ \frac{31}{312} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 8x+\frac{6}{5}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{+12} & = & \color{red}{-30x} +15 \\\Leftrightarrow & 80x \color{red}{+12} \color{blue}{-12} \color{blue}{+30x} & = & \color{red}{-30x} +15 \color{blue}{+30x} \color{blue}{-12} \\\Leftrightarrow & 80x+30x& = & 15-12 \\\Leftrightarrow & \color{red}{110} x& = & 3 \\\Leftrightarrow & x = \frac{3}{110} & & \\ & V = \left\{ \frac{3}{110} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{9})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -16x+\frac{20}{9}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-288}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -288x \color{red}{+40} & = & \color{red}{-126x} +27 \\\Leftrightarrow & -288x \color{red}{+40} \color{blue}{-40} \color{blue}{+126x} & = & \color{red}{-126x} +27 \color{blue}{+126x} \color{blue}{-40} \\\Leftrightarrow & -288x+126x& = & 27-40 \\\Leftrightarrow & \color{red}{-162} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-162} & & \\\Leftrightarrow & x = \frac{13}{162} & & \\ & V = \left\{ \frac{13}{162} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{8}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{88}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-88} & = & \color{red}{-385x} +70 \\\Leftrightarrow & 924x \color{red}{-88} \color{blue}{+88} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{+88} \\\Leftrightarrow & 924x+385x& = & 70+88 \\\Leftrightarrow & \color{red}{1309} x& = & 158 \\\Leftrightarrow & x = \frac{158}{1309} & & \\ & V = \left\{ \frac{158}{1309} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{11})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 14x-\frac{14}{11}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{308}{ \color{blue}{22} }x- \frac{28}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 308x \color{red}{-28} & = & \color{red}{-66x} +55 \\\Leftrightarrow & 308x \color{red}{-28} \color{blue}{+28} \color{blue}{+66x} & = & \color{red}{-66x} +55 \color{blue}{+66x} \color{blue}{+28} \\\Leftrightarrow & 308x+66x& = & 55+28 \\\Leftrightarrow & \color{red}{374} x& = & 83 \\\Leftrightarrow & x = \frac{83}{374} & & \\ & V = \left\{ \frac{83}{374} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 8x+\frac{7}{2} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-40} & = & \color{red}{48x} +21 \\\Leftrightarrow & 90x \color{red}{-40} \color{blue}{+40} \color{blue}{-48x} & = & \color{red}{48x} +21 \color{blue}{-48x} \color{blue}{+40} \\\Leftrightarrow & 90x-48x& = & 21+40 \\\Leftrightarrow & \color{red}{42} x& = & 61 \\\Leftrightarrow & x = \frac{61}{42} & & \\ & V = \left\{ \frac{61}{42} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -720x \color{red}{+144} & = & \color{red}{300x} +25 \\\Leftrightarrow & -720x \color{red}{+144} \color{blue}{-144} \color{blue}{-300x} & = & \color{red}{300x} +25 \color{blue}{-300x} \color{blue}{-144} \\\Leftrightarrow & -720x-300x& = & 25-144 \\\Leftrightarrow & \color{red}{-1020} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-1020} & & \\\Leftrightarrow & x = \frac{7}{60} & & \\ & V = \left\{ \frac{7}{60} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{8}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{24}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-24} & = & \color{red}{75x} +50 \\\Leftrightarrow & -180x \color{red}{-24} \color{blue}{+24} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+24} \\\Leftrightarrow & -180x-75x& = & 50+24 \\\Leftrightarrow & \color{red}{-255} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-255} & & \\\Leftrightarrow & x = \frac{-74}{255} & & \\ & V = \left\{ \frac{-74}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+6} & = & \color{red}{49x} +2 \\\Leftrightarrow & 56x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & 56x-49x& = & 2-6 \\\Leftrightarrow & \color{red}{7} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{7} & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{-162} & = & \color{red}{693x} +44 \\\Leftrightarrow & 2376x \color{red}{-162} \color{blue}{+162} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{+162} \\\Leftrightarrow & 2376x-693x& = & 44+162 \\\Leftrightarrow & \color{red}{1683} x& = & 206 \\\Leftrightarrow & x = \frac{206}{1683} & & \\ & V = \left\{ \frac{206}{1683} \right\} & \\\end{align}\)