Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & -7x+\frac{7}{12} \\\Leftrightarrow & 8x+\frac{4}{3}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{+16} & = & \color{red}{-84x} +7 \\\Leftrightarrow & 96x \color{red}{+16} \color{blue}{-16} \color{blue}{+84x} & = & \color{red}{-84x} +7 \color{blue}{+84x} \color{blue}{-16} \\\Leftrightarrow & 96x+84x& = & 7-16 \\\Leftrightarrow & \color{red}{180} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{180} & & \\\Leftrightarrow & x = \frac{-1}{20} & & \\ & V = \left\{ \frac{-1}{20} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{3})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -16x-\frac{16}{3}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-112} & = & \color{red}{147x} +27 \\\Leftrightarrow & -336x \color{red}{-112} \color{blue}{+112} \color{blue}{-147x} & = & \color{red}{147x} +27 \color{blue}{-147x} \color{blue}{+112} \\\Leftrightarrow & -336x-147x& = & 27+112 \\\Leftrightarrow & \color{red}{-483} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-483} & & \\\Leftrightarrow & x = \frac{-139}{483} & & \\ & V = \left\{ \frac{-139}{483} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & 9x+\frac{7}{12} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1512}{ \color{blue}{84} }x+ \frac{360}{ \color{blue}{84} })& = & (\frac{756}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1512x \color{red}{+360} & = & \color{red}{756x} +49 \\\Leftrightarrow & -1512x \color{red}{+360} \color{blue}{-360} \color{blue}{-756x} & = & \color{red}{756x} +49 \color{blue}{-756x} \color{blue}{-360} \\\Leftrightarrow & -1512x-756x& = & 49-360 \\\Leftrightarrow & \color{red}{-2268} x& = & -311 \\\Leftrightarrow & x = \frac{-311}{-2268} & & \\\Leftrightarrow & x = \frac{311}{2268} & & \\ & V = \left\{ \frac{311}{2268} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+10} & = & \color{red}{35x} +10 \\\Leftrightarrow & 42x \color{red}{+10} \color{blue}{-10} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-10} \\\Leftrightarrow & 42x-35x& = & 10-10 \\\Leftrightarrow & \color{red}{7} x& = & 0 \\\Leftrightarrow & x = \frac{0}{7} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{6})& = & 2x+\frac{5}{8} \\\Leftrightarrow & 21x-\frac{35}{6}& = & 2x+\frac{5}{8} \\ & & & \text{kgv van noemers 6 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x- \frac{140}{ \color{blue}{24} })& = & (\frac{48}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{-140} & = & \color{red}{48x} +15 \\\Leftrightarrow & 504x \color{red}{-140} \color{blue}{+140} \color{blue}{-48x} & = & \color{red}{48x} +15 \color{blue}{-48x} \color{blue}{+140} \\\Leftrightarrow & 504x-48x& = & 15+140 \\\Leftrightarrow & \color{red}{456} x& = & 155 \\\Leftrightarrow & x = \frac{155}{456} & & \\ & V = \left\{ \frac{155}{456} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 20x+\frac{10}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+20} & = & \color{red}{-154x} +33 \\\Leftrightarrow & 440x \color{red}{+20} \color{blue}{-20} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{-20} \\\Leftrightarrow & 440x+154x& = & 33-20 \\\Leftrightarrow & \color{red}{594} x& = & 13 \\\Leftrightarrow & x = \frac{13}{594} & & \\ & V = \left\{ \frac{13}{594} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 12x-\frac{9}{5}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-81} & = & \color{red}{225x} +25 \\\Leftrightarrow & 540x \color{red}{-81} \color{blue}{+81} \color{blue}{-225x} & = & \color{red}{225x} +25 \color{blue}{-225x} \color{blue}{+81} \\\Leftrightarrow & 540x-225x& = & 25+81 \\\Leftrightarrow & \color{red}{315} x& = & 106 \\\Leftrightarrow & x = \frac{106}{315} & & \\ & V = \left\{ \frac{106}{315} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-240}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -240x \color{red}{+24} & = & \color{red}{70x} +7 \\\Leftrightarrow & -240x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +7 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -240x-70x& = & 7-24 \\\Leftrightarrow & \color{red}{-310} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-310} & & \\\Leftrightarrow & x = \frac{17}{310} & & \\ & V = \left\{ \frac{17}{310} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & 8x+\frac{2}{11} \\\Leftrightarrow & -21x-\frac{14}{9}& = & 8x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2079}{ \color{blue}{99} }x- \frac{154}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2079x \color{red}{-154} & = & \color{red}{792x} +18 \\\Leftrightarrow & -2079x \color{red}{-154} \color{blue}{+154} \color{blue}{-792x} & = & \color{red}{792x} +18 \color{blue}{-792x} \color{blue}{+154} \\\Leftrightarrow & -2079x-792x& = & 18+154 \\\Leftrightarrow & \color{red}{-2871} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-2871} & & \\\Leftrightarrow & x = \frac{-172}{2871} & & \\ & V = \left\{ \frac{-172}{2871} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{-231x} +22 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & -330x+231x& = & 22+30 \\\Leftrightarrow & \color{red}{-99} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-99} & & \\\Leftrightarrow & x = \frac{-52}{99} & & \\ & V = \left\{ \frac{-52}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{4})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -14x+\frac{21}{4}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-616}{ \color{blue}{44} }x+ \frac{231}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{20}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -616x \color{red}{+231} & = & \color{red}{132x} +20 \\\Leftrightarrow & -616x \color{red}{+231} \color{blue}{-231} \color{blue}{-132x} & = & \color{red}{132x} +20 \color{blue}{-132x} \color{blue}{-231} \\\Leftrightarrow & -616x-132x& = & 20-231 \\\Leftrightarrow & \color{red}{-748} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{-748} & & \\\Leftrightarrow & x = \frac{211}{748} & & \\ & V = \left\{ \frac{211}{748} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{11})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 28x+\frac{21}{11}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2156}{ \color{blue}{77} }x+ \frac{147}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2156x \color{red}{+147} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 2156x \color{red}{+147} \color{blue}{-147} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-147} \\\Leftrightarrow & 2156x+385x& = & 66-147 \\\Leftrightarrow & \color{red}{2541} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{2541} & & \\\Leftrightarrow & x = \frac{-27}{847} & & \\ & V = \left\{ \frac{-27}{847} \right\} & \\\end{align}\)