Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -4x+\frac{7}{9} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -4x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-180}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{-108} & = & \color{red}{-180x} +35 \\\Leftrightarrow & 675x \color{red}{-108} \color{blue}{+108} \color{blue}{+180x} & = & \color{red}{-180x} +35 \color{blue}{+180x} \color{blue}{+108} \\\Leftrightarrow & 675x+180x& = & 35+108 \\\Leftrightarrow & \color{red}{855} x& = & 143 \\\Leftrightarrow & x = \frac{143}{855} & & \\ & V = \left\{ \frac{143}{855} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{2})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{25}{2}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+225} & = & \color{red}{-126x} +4 \\\Leftrightarrow & 360x \color{red}{+225} \color{blue}{-225} \color{blue}{+126x} & = & \color{red}{-126x} +4 \color{blue}{+126x} \color{blue}{-225} \\\Leftrightarrow & 360x+126x& = & 4-225 \\\Leftrightarrow & \color{red}{486} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{486} & & \\ & V = \left\{ \frac{-221}{486} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{9})& = & 9x+\frac{4}{9} \\\Leftrightarrow & -25x+\frac{10}{9}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{+10} & = & \color{red}{81x} +4 \\\Leftrightarrow & -225x \color{red}{+10} \color{blue}{-10} \color{blue}{-81x} & = & \color{red}{81x} +4 \color{blue}{-81x} \color{blue}{-10} \\\Leftrightarrow & -225x-81x& = & 4-10 \\\Leftrightarrow & \color{red}{-306} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-306} & & \\\Leftrightarrow & x = \frac{1}{51} & & \\ & V = \left\{ \frac{1}{51} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{11})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 30x+\frac{30}{11}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{+30} & = & \color{red}{-77x} +4 \\\Leftrightarrow & 330x \color{red}{+30} \color{blue}{-30} \color{blue}{+77x} & = & \color{red}{-77x} +4 \color{blue}{+77x} \color{blue}{-30} \\\Leftrightarrow & 330x+77x& = & 4-30 \\\Leftrightarrow & \color{red}{407} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{407} & & \\ & V = \left\{ \frac{-26}{407} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -9x+\frac{6}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{+12} & = & \color{red}{70x} +49 \\\Leftrightarrow & -126x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & -126x-70x& = & 49-12 \\\Leftrightarrow & \color{red}{-196} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-196} & & \\\Leftrightarrow & x = \frac{-37}{196} & & \\ & V = \left\{ \frac{-37}{196} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{8})& = & -4x+\frac{8}{3} \\\Leftrightarrow & 25x-\frac{15}{8}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{-45} & = & \color{red}{-96x} +64 \\\Leftrightarrow & 600x \color{red}{-45} \color{blue}{+45} \color{blue}{+96x} & = & \color{red}{-96x} +64 \color{blue}{+96x} \color{blue}{+45} \\\Leftrightarrow & 600x+96x& = & 64+45 \\\Leftrightarrow & \color{red}{696} x& = & 109 \\\Leftrightarrow & x = \frac{109}{696} & & \\ & V = \left\{ \frac{109}{696} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{-539x} +49 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +49 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & -770x+539x& = & 49+110 \\\Leftrightarrow & \color{red}{-231} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-231} & & \\\Leftrightarrow & x = \frac{-53}{77} & & \\ & V = \left\{ \frac{-53}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & 8x+\frac{5}{11} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{-154} & = & \color{red}{264x} +15 \\\Leftrightarrow & -693x \color{red}{-154} \color{blue}{+154} \color{blue}{-264x} & = & \color{red}{264x} +15 \color{blue}{-264x} \color{blue}{+154} \\\Leftrightarrow & -693x-264x& = & 15+154 \\\Leftrightarrow & \color{red}{-957} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-957} & & \\\Leftrightarrow & x = \frac{-169}{957} & & \\ & V = \left\{ \frac{-169}{957} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{9})& = & 3x+\frac{7}{10} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 3x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-720}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -720x \color{red}{-80} & = & \color{red}{270x} +63 \\\Leftrightarrow & -720x \color{red}{-80} \color{blue}{+80} \color{blue}{-270x} & = & \color{red}{270x} +63 \color{blue}{-270x} \color{blue}{+80} \\\Leftrightarrow & -720x-270x& = & 63+80 \\\Leftrightarrow & \color{red}{-990} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-990} & & \\\Leftrightarrow & x = \frac{-13}{90} & & \\ & V = \left\{ \frac{-13}{90} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-150} & = & \color{red}{-245x} +63 \\\Leftrightarrow & 1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +63 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & 1050x+245x& = & 63+150 \\\Leftrightarrow & \color{red}{1295} x& = & 213 \\\Leftrightarrow & x = \frac{213}{1295} & & \\ & V = \left\{ \frac{213}{1295} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{20}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+20} & = & \color{red}{-77x} +6 \\\Leftrightarrow & 220x \color{red}{+20} \color{blue}{-20} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{-20} \\\Leftrightarrow & 220x+77x& = & 6-20 \\\Leftrightarrow & \color{red}{297} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{297} & & \\ & V = \left\{ \frac{-14}{297} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-48} & = & \color{red}{-280x} +49 \\\Leftrightarrow & 672x \color{red}{-48} \color{blue}{+48} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{+48} \\\Leftrightarrow & 672x+280x& = & 49+48 \\\Leftrightarrow & \color{red}{952} x& = & 97 \\\Leftrightarrow & x = \frac{97}{952} & & \\ & V = \left\{ \frac{97}{952} \right\} & \\\end{align}\)